diff --git a/src/compiler/checker.ts b/src/compiler/checker.ts
index a5c161abae051..f9350010c2a5e 100644
--- a/src/compiler/checker.ts
+++ b/src/compiler/checker.ts
@@ -21025,7 +21025,7 @@ export function createTypeChecker(host: TypeCheckerHost): TypeChecker {
     }
 
     function hasContextSensitiveReturnExpression(node: FunctionLikeDeclaration) {
-        if (node.typeParameters || getEffectiveReturnTypeNode(node) || !node.body) {
+        if (getEffectiveReturnTypeNode(node) || !node.body) {
             return false;
         }
         if (node.body.kind !== SyntaxKind.Block) {
diff --git a/src/compiler/utilities.ts b/src/compiler/utilities.ts
index ce3182ddd9d40..2729d846d974e 100644
--- a/src/compiler/utilities.ts
+++ b/src/compiler/utilities.ts
@@ -10783,20 +10783,17 @@ export function getContainingNodeArray(node: Node): NodeArray<Node> | undefined
 
 /** @internal */
 export function hasContextSensitiveParameters(node: FunctionLikeDeclaration): boolean {
-    // Functions with type parameters are not context sensitive.
-    if (!node.typeParameters) {
-        // Functions with any parameters that lack type annotations are context sensitive.
-        if (some(node.parameters, p => !getEffectiveTypeAnnotationNode(p))) {
+    // Functions with any parameters that lack type annotations are context sensitive.
+    if (some(node.parameters, p => !getEffectiveTypeAnnotationNode(p))) {
+        return true;
+    }
+    if (node.kind !== SyntaxKind.ArrowFunction) {
+        // If the first parameter is not an explicit 'this' parameter, then the function has
+        // an implicit 'this' parameter which is subject to contextual typing.
+        const parameter = firstOrUndefined(node.parameters);
+        if (!(parameter && parameterIsThisKeyword(parameter))) {
             return true;
         }
-        if (node.kind !== SyntaxKind.ArrowFunction) {
-            // If the first parameter is not an explicit 'this' parameter, then the function has
-            // an implicit 'this' parameter which is subject to contextual typing.
-            const parameter = firstOrUndefined(node.parameters);
-            if (!(parameter && parameterIsThisKeyword(parameter))) {
-                return true;
-            }
-        }
     }
     return false;
 }
diff --git a/tests/baselines/reference/contextualTypingGenericFunction2.js b/tests/baselines/reference/contextualTypingGenericFunction2.js
new file mode 100644
index 0000000000000..5f06aa6fc7b8b
--- /dev/null
+++ b/tests/baselines/reference/contextualTypingGenericFunction2.js
@@ -0,0 +1,89 @@
+//// [tests/cases/compiler/contextualTypingGenericFunction2.ts] ////
+
+//// [contextualTypingGenericFunction2.ts]
+// https://github.com/microsoft/TypeScript/issues/61791
+
+declare const fn1: <T, Args extends Array<any>, Ret>(
+  self: T,
+  body: (this: T, ...args: Args) => Ret,
+) => (...args: Args) => Ret;
+
+export const ok1 = fn1({ message: "foo" }, function (n: number) {
+  this.message;
+});
+
+export const ok2 = fn1({ message: "foo" }, function <N>(n: N) {
+  this.message;
+});
+
+declare const fn2: <Args extends Array<any>, Ret>(
+  body: (first: string, ...args: Args) => Ret,
+) => (...args: Args) => Ret;
+
+export const ok3 = fn2(function <N>(first, n: N) {});
+
+declare const fn3: <Args extends Array<any>, Ret>(
+  body: (...args: Args) => (arg: string) => Ret,
+) => (...args: Args) => Ret;
+
+export const ok4 = fn3(function <N>(n: N) {
+    return (arg) => {
+        return 10
+    }
+});
+
+declare function fn4<T, P>(config: {
+  context: T;
+  callback: (params: P) => (context: T, params: P) => number;
+}): (params: P) => number;
+
+export const ok5 = fn4({
+  context: 1,
+  callback: <T,>(params: T) => {
+    return (a, b) => a + 1;
+  },
+});
+
+declare const fnGen1: <T, Args extends Array<any>, Ret>(
+  self: T,
+  body: (this: T, ...args: Args) => Generator<any, Ret, never>,
+) => (...args: Args) => Ret;
+
+export const ok6 = fnGen1({ message: "foo" }, function* (n: number) {
+  this.message;
+});
+
+export const ok7 = fnGen1({ message: "foo" }, function* <N>(n: N) {
+  this.message;
+});
+
+
+
+
+//// [contextualTypingGenericFunction2.d.ts]
+export declare const ok1: (n: number) => void;
+export declare const ok2: (n: any) => void;
+export declare const ok3: <N>(n: N) => void;
+export declare const ok4: <N>(n: N) => number;
+export declare const ok5: (params: T) => number;
+export declare const ok6: (n: number) => void;
+export declare const ok7: (n: any) => void;
+
+
+//// [DtsFileErrors]
+
+
+contextualTypingGenericFunction2.d.ts(5,36): error TS2304: Cannot find name 'T'.
+
+
+==== contextualTypingGenericFunction2.d.ts (1 errors) ====
+    export declare const ok1: (n: number) => void;
+    export declare const ok2: (n: any) => void;
+    export declare const ok3: <N>(n: N) => void;
+    export declare const ok4: <N>(n: N) => number;
+    export declare const ok5: (params: T) => number;
+                                       ~
+!!! error TS2304: Cannot find name 'T'.
+    export declare const ok6: (n: number) => void;
+    export declare const ok7: (n: any) => void;
+    
\ No newline at end of file
diff --git a/tests/baselines/reference/contextualTypingGenericFunction2.symbols b/tests/baselines/reference/contextualTypingGenericFunction2.symbols
new file mode 100644
index 0000000000000..16c60357bd75f
--- /dev/null
+++ b/tests/baselines/reference/contextualTypingGenericFunction2.symbols
@@ -0,0 +1,212 @@
+//// [tests/cases/compiler/contextualTypingGenericFunction2.ts] ////
+
+=== contextualTypingGenericFunction2.ts ===
+// https://github.com/microsoft/TypeScript/issues/61791
+
+declare const fn1: <T, Args extends Array<any>, Ret>(
+>fn1 : Symbol(fn1, Decl(contextualTypingGenericFunction2.ts, 2, 13))
+>T : Symbol(T, Decl(contextualTypingGenericFunction2.ts, 2, 20))
+>Args : Symbol(Args, Decl(contextualTypingGenericFunction2.ts, 2, 22))
+>Array : Symbol(Array, Decl(lib.es5.d.ts, --, --), Decl(lib.es5.d.ts, --, --), Decl(lib.es2015.core.d.ts, --, --), Decl(lib.es2015.iterable.d.ts, --, --), Decl(lib.es2015.symbol.wellknown.d.ts, --, --) ... and 4 more)
+>Ret : Symbol(Ret, Decl(contextualTypingGenericFunction2.ts, 2, 47))
+
+  self: T,
+>self : Symbol(self, Decl(contextualTypingGenericFunction2.ts, 2, 53))
+>T : Symbol(T, Decl(contextualTypingGenericFunction2.ts, 2, 20))
+
+  body: (this: T, ...args: Args) => Ret,
+>body : Symbol(body, Decl(contextualTypingGenericFunction2.ts, 3, 10))
+>this : Symbol(this, Decl(contextualTypingGenericFunction2.ts, 4, 9))
+>T : Symbol(T, Decl(contextualTypingGenericFunction2.ts, 2, 20))
+>args : Symbol(args, Decl(contextualTypingGenericFunction2.ts, 4, 17))
+>Args : Symbol(Args, Decl(contextualTypingGenericFunction2.ts, 2, 22))
+>Ret : Symbol(Ret, Decl(contextualTypingGenericFunction2.ts, 2, 47))
+
+) => (...args: Args) => Ret;
+>args : Symbol(args, Decl(contextualTypingGenericFunction2.ts, 5, 6))
+>Args : Symbol(Args, Decl(contextualTypingGenericFunction2.ts, 2, 22))
+>Ret : Symbol(Ret, Decl(contextualTypingGenericFunction2.ts, 2, 47))
+
+export const ok1 = fn1({ message: "foo" }, function (n: number) {
+>ok1 : Symbol(ok1, Decl(contextualTypingGenericFunction2.ts, 7, 12))
+>fn1 : Symbol(fn1, Decl(contextualTypingGenericFunction2.ts, 2, 13))
+>message : Symbol(message, Decl(contextualTypingGenericFunction2.ts, 7, 24))
+>n : Symbol(n, Decl(contextualTypingGenericFunction2.ts, 7, 53))
+
+  this.message;
+>this.message : Symbol(message, Decl(contextualTypingGenericFunction2.ts, 7, 24))
+>this : Symbol(this, Decl(contextualTypingGenericFunction2.ts, 4, 9))
+>message : Symbol(message, Decl(contextualTypingGenericFunction2.ts, 7, 24))
+
+});
+
+export const ok2 = fn1({ message: "foo" }, function <N>(n: N) {
+>ok2 : Symbol(ok2, Decl(contextualTypingGenericFunction2.ts, 11, 12))
+>fn1 : Symbol(fn1, Decl(contextualTypingGenericFunction2.ts, 2, 13))
+>message : Symbol(message, Decl(contextualTypingGenericFunction2.ts, 11, 24))
+>N : Symbol(N, Decl(contextualTypingGenericFunction2.ts, 11, 53))
+>n : Symbol(n, Decl(contextualTypingGenericFunction2.ts, 11, 56))
+>N : Symbol(N, Decl(contextualTypingGenericFunction2.ts, 11, 53))
+
+  this.message;
+>this.message : Symbol(message, Decl(contextualTypingGenericFunction2.ts, 11, 24))
+>this : Symbol(this, Decl(contextualTypingGenericFunction2.ts, 4, 9))
+>message : Symbol(message, Decl(contextualTypingGenericFunction2.ts, 11, 24))
+
+});
+
+declare const fn2: <Args extends Array<any>, Ret>(
+>fn2 : Symbol(fn2, Decl(contextualTypingGenericFunction2.ts, 15, 13))
+>Args : Symbol(Args, Decl(contextualTypingGenericFunction2.ts, 15, 20))
+>Array : Symbol(Array, Decl(lib.es5.d.ts, --, --), Decl(lib.es5.d.ts, --, --), Decl(lib.es2015.core.d.ts, --, --), Decl(lib.es2015.iterable.d.ts, --, --), Decl(lib.es2015.symbol.wellknown.d.ts, --, --) ... and 4 more)
+>Ret : Symbol(Ret, Decl(contextualTypingGenericFunction2.ts, 15, 44))
+
+  body: (first: string, ...args: Args) => Ret,
+>body : Symbol(body, Decl(contextualTypingGenericFunction2.ts, 15, 50))
+>first : Symbol(first, Decl(contextualTypingGenericFunction2.ts, 16, 9))
+>args : Symbol(args, Decl(contextualTypingGenericFunction2.ts, 16, 23))
+>Args : Symbol(Args, Decl(contextualTypingGenericFunction2.ts, 15, 20))
+>Ret : Symbol(Ret, Decl(contextualTypingGenericFunction2.ts, 15, 44))
+
+) => (...args: Args) => Ret;
+>args : Symbol(args, Decl(contextualTypingGenericFunction2.ts, 17, 6))
+>Args : Symbol(Args, Decl(contextualTypingGenericFunction2.ts, 15, 20))
+>Ret : Symbol(Ret, Decl(contextualTypingGenericFunction2.ts, 15, 44))
+
+export const ok3 = fn2(function <N>(first, n: N) {});
+>ok3 : Symbol(ok3, Decl(contextualTypingGenericFunction2.ts, 19, 12))
+>fn2 : Symbol(fn2, Decl(contextualTypingGenericFunction2.ts, 15, 13))
+>N : Symbol(N, Decl(contextualTypingGenericFunction2.ts, 19, 33))
+>first : Symbol(first, Decl(contextualTypingGenericFunction2.ts, 19, 36))
+>n : Symbol(n, Decl(contextualTypingGenericFunction2.ts, 19, 42))
+>N : Symbol(N, Decl(contextualTypingGenericFunction2.ts, 19, 33))
+
+declare const fn3: <Args extends Array<any>, Ret>(
+>fn3 : Symbol(fn3, Decl(contextualTypingGenericFunction2.ts, 21, 13))
+>Args : Symbol(Args, Decl(contextualTypingGenericFunction2.ts, 21, 20))
+>Array : Symbol(Array, Decl(lib.es5.d.ts, --, --), Decl(lib.es5.d.ts, --, --), Decl(lib.es2015.core.d.ts, --, --), Decl(lib.es2015.iterable.d.ts, --, --), Decl(lib.es2015.symbol.wellknown.d.ts, --, --) ... and 4 more)
+>Ret : Symbol(Ret, Decl(contextualTypingGenericFunction2.ts, 21, 44))
+
+  body: (...args: Args) => (arg: string) => Ret,
+>body : Symbol(body, Decl(contextualTypingGenericFunction2.ts, 21, 50))
+>args : Symbol(args, Decl(contextualTypingGenericFunction2.ts, 22, 9))
+>Args : Symbol(Args, Decl(contextualTypingGenericFunction2.ts, 21, 20))
+>arg : Symbol(arg, Decl(contextualTypingGenericFunction2.ts, 22, 28))
+>Ret : Symbol(Ret, Decl(contextualTypingGenericFunction2.ts, 21, 44))
+
+) => (...args: Args) => Ret;
+>args : Symbol(args, Decl(contextualTypingGenericFunction2.ts, 23, 6))
+>Args : Symbol(Args, Decl(contextualTypingGenericFunction2.ts, 21, 20))
+>Ret : Symbol(Ret, Decl(contextualTypingGenericFunction2.ts, 21, 44))
+
+export const ok4 = fn3(function <N>(n: N) {
+>ok4 : Symbol(ok4, Decl(contextualTypingGenericFunction2.ts, 25, 12))
+>fn3 : Symbol(fn3, Decl(contextualTypingGenericFunction2.ts, 21, 13))
+>N : Symbol(N, Decl(contextualTypingGenericFunction2.ts, 25, 33))
+>n : Symbol(n, Decl(contextualTypingGenericFunction2.ts, 25, 36))
+>N : Symbol(N, Decl(contextualTypingGenericFunction2.ts, 25, 33))
+
+    return (arg) => {
+>arg : Symbol(arg, Decl(contextualTypingGenericFunction2.ts, 26, 12))
+
+        return 10
+    }
+});
+
+declare function fn4<T, P>(config: {
+>fn4 : Symbol(fn4, Decl(contextualTypingGenericFunction2.ts, 29, 3))
+>T : Symbol(T, Decl(contextualTypingGenericFunction2.ts, 31, 21))
+>P : Symbol(P, Decl(contextualTypingGenericFunction2.ts, 31, 23))
+>config : Symbol(config, Decl(contextualTypingGenericFunction2.ts, 31, 27))
+
+  context: T;
+>context : Symbol(context, Decl(contextualTypingGenericFunction2.ts, 31, 36))
+>T : Symbol(T, Decl(contextualTypingGenericFunction2.ts, 31, 21))
+
+  callback: (params: P) => (context: T, params: P) => number;
+>callback : Symbol(callback, Decl(contextualTypingGenericFunction2.ts, 32, 13))
+>params : Symbol(params, Decl(contextualTypingGenericFunction2.ts, 33, 13))
+>P : Symbol(P, Decl(contextualTypingGenericFunction2.ts, 31, 23))
+>context : Symbol(context, Decl(contextualTypingGenericFunction2.ts, 33, 28))
+>T : Symbol(T, Decl(contextualTypingGenericFunction2.ts, 31, 21))
+>params : Symbol(params, Decl(contextualTypingGenericFunction2.ts, 33, 39))
+>P : Symbol(P, Decl(contextualTypingGenericFunction2.ts, 31, 23))
+
+}): (params: P) => number;
+>params : Symbol(params, Decl(contextualTypingGenericFunction2.ts, 34, 5))
+>P : Symbol(P, Decl(contextualTypingGenericFunction2.ts, 31, 23))
+
+export const ok5 = fn4({
+>ok5 : Symbol(ok5, Decl(contextualTypingGenericFunction2.ts, 36, 12))
+>fn4 : Symbol(fn4, Decl(contextualTypingGenericFunction2.ts, 29, 3))
+
+  context: 1,
+>context : Symbol(context, Decl(contextualTypingGenericFunction2.ts, 36, 24))
+
+  callback: <T,>(params: T) => {
+>callback : Symbol(callback, Decl(contextualTypingGenericFunction2.ts, 37, 13))
+>T : Symbol(T, Decl(contextualTypingGenericFunction2.ts, 38, 13))
+>params : Symbol(params, Decl(contextualTypingGenericFunction2.ts, 38, 17))
+>T : Symbol(T, Decl(contextualTypingGenericFunction2.ts, 38, 13))
+
+    return (a, b) => a + 1;
+>a : Symbol(a, Decl(contextualTypingGenericFunction2.ts, 39, 12))
+>b : Symbol(b, Decl(contextualTypingGenericFunction2.ts, 39, 14))
+>a : Symbol(a, Decl(contextualTypingGenericFunction2.ts, 39, 12))
+
+  },
+});
+
+declare const fnGen1: <T, Args extends Array<any>, Ret>(
+>fnGen1 : Symbol(fnGen1, Decl(contextualTypingGenericFunction2.ts, 43, 13))
+>T : Symbol(T, Decl(contextualTypingGenericFunction2.ts, 43, 23))
+>Args : Symbol(Args, Decl(contextualTypingGenericFunction2.ts, 43, 25))
+>Array : Symbol(Array, Decl(lib.es5.d.ts, --, --), Decl(lib.es5.d.ts, --, --), Decl(lib.es2015.core.d.ts, --, --), Decl(lib.es2015.iterable.d.ts, --, --), Decl(lib.es2015.symbol.wellknown.d.ts, --, --) ... and 4 more)
+>Ret : Symbol(Ret, Decl(contextualTypingGenericFunction2.ts, 43, 50))
+
+  self: T,
+>self : Symbol(self, Decl(contextualTypingGenericFunction2.ts, 43, 56))
+>T : Symbol(T, Decl(contextualTypingGenericFunction2.ts, 43, 23))
+
+  body: (this: T, ...args: Args) => Generator<any, Ret, never>,
+>body : Symbol(body, Decl(contextualTypingGenericFunction2.ts, 44, 10))
+>this : Symbol(this, Decl(contextualTypingGenericFunction2.ts, 45, 9))
+>T : Symbol(T, Decl(contextualTypingGenericFunction2.ts, 43, 23))
+>args : Symbol(args, Decl(contextualTypingGenericFunction2.ts, 45, 17))
+>Args : Symbol(Args, Decl(contextualTypingGenericFunction2.ts, 43, 25))
+>Generator : Symbol(Generator, Decl(lib.es2015.generator.d.ts, --, --))
+>Ret : Symbol(Ret, Decl(contextualTypingGenericFunction2.ts, 43, 50))
+
+) => (...args: Args) => Ret;
+>args : Symbol(args, Decl(contextualTypingGenericFunction2.ts, 46, 6))
+>Args : Symbol(Args, Decl(contextualTypingGenericFunction2.ts, 43, 25))
+>Ret : Symbol(Ret, Decl(contextualTypingGenericFunction2.ts, 43, 50))
+
+export const ok6 = fnGen1({ message: "foo" }, function* (n: number) {
+>ok6 : Symbol(ok6, Decl(contextualTypingGenericFunction2.ts, 48, 12))
+>fnGen1 : Symbol(fnGen1, Decl(contextualTypingGenericFunction2.ts, 43, 13))
+>message : Symbol(message, Decl(contextualTypingGenericFunction2.ts, 48, 27))
+>n : Symbol(n, Decl(contextualTypingGenericFunction2.ts, 48, 57))
+
+  this.message;
+>this.message : Symbol(message, Decl(contextualTypingGenericFunction2.ts, 48, 27))
+>this : Symbol(this, Decl(contextualTypingGenericFunction2.ts, 45, 9))
+>message : Symbol(message, Decl(contextualTypingGenericFunction2.ts, 48, 27))
+
+});
+
+export const ok7 = fnGen1({ message: "foo" }, function* <N>(n: N) {
+>ok7 : Symbol(ok7, Decl(contextualTypingGenericFunction2.ts, 52, 12))
+>fnGen1 : Symbol(fnGen1, Decl(contextualTypingGenericFunction2.ts, 43, 13))
+>message : Symbol(message, Decl(contextualTypingGenericFunction2.ts, 52, 27))
+>N : Symbol(N, Decl(contextualTypingGenericFunction2.ts, 52, 57))
+>n : Symbol(n, Decl(contextualTypingGenericFunction2.ts, 52, 60))
+>N : Symbol(N, Decl(contextualTypingGenericFunction2.ts, 52, 57))
+
+  this.message;
+>this.message : Symbol(message, Decl(contextualTypingGenericFunction2.ts, 52, 27))
+>this : Symbol(this, Decl(contextualTypingGenericFunction2.ts, 45, 9))
+>message : Symbol(message, Decl(contextualTypingGenericFunction2.ts, 52, 27))
+
+});
+
diff --git a/tests/baselines/reference/contextualTypingGenericFunction2.types b/tests/baselines/reference/contextualTypingGenericFunction2.types
new file mode 100644
index 0000000000000..970aef92e6806
--- /dev/null
+++ b/tests/baselines/reference/contextualTypingGenericFunction2.types
@@ -0,0 +1,296 @@
+//// [tests/cases/compiler/contextualTypingGenericFunction2.ts] ////
+
+=== Performance Stats ===
+Type Count: 1,000
+Instantiation count: 2,500
+
+=== contextualTypingGenericFunction2.ts ===
+// https://github.com/microsoft/TypeScript/issues/61791
+
+declare const fn1: <T, Args extends Array<any>, Ret>(
+>fn1 : <T, Args extends Array<any>, Ret>(self: T, body: (this: T, ...args: Args) => Ret) => (...args: Args) => Ret
+>    : ^ ^^    ^^^^^^^^^          ^^   ^^    ^^ ^^    ^^                               ^^^^^                      
+
+  self: T,
+>self : T
+>     : ^
+
+  body: (this: T, ...args: Args) => Ret,
+>body : (this: T, ...args: Args) => Ret
+>     : ^    ^^ ^^^^^    ^^    ^^^^^   
+>this : T
+>     : ^
+>args : Args
+>     : ^^^^
+
+) => (...args: Args) => Ret;
+>args : Args
+>     : ^^^^
+
+export const ok1 = fn1({ message: "foo" }, function (n: number) {
+>ok1 : (n: number) => void
+>    : ^^^^^^^^^^^^^^^^^^^
+>fn1({ message: "foo" }, function (n: number) {  this.message;}) : (n: number) => void
+>                                                                : ^^^^^^^^^^^^^^^^^^^
+>fn1 : <T, Args extends Array<any>, Ret>(self: T, body: (this: T, ...args: Args) => Ret) => (...args: Args) => Ret
+>    : ^ ^^    ^^^^^^^^^          ^^   ^^    ^^ ^^    ^^                               ^^^^^                      
+>{ message: "foo" } : { message: string; }
+>                   : ^^^^^^^^^^^^^^^^^^^^
+>message : string
+>        : ^^^^^^
+>"foo" : "foo"
+>      : ^^^^^
+>function (n: number) {  this.message;} : (this: { message: string; }, n: number) => void
+>                                       : ^    ^^^^^^^^^^^^^^^^^^^^^^^^ ^^      ^^^^^^^^^
+>n : number
+>  : ^^^^^^
+
+  this.message;
+>this.message : string
+>             : ^^^^^^
+>this : { message: string; }
+>     : ^^^^^^^^^^^^^^^^^^^^
+>message : string
+>        : ^^^^^^
+
+});
+
+export const ok2 = fn1({ message: "foo" }, function <N>(n: N) {
+>ok2 : (n: any) => void
+>    : ^^^^^^^^^^^^^^^^
+>fn1({ message: "foo" }, function <N>(n: N) {  this.message;}) : (n: any) => void
+>                                                              : ^^^^^^^^^^^^^^^^
+>fn1 : <T, Args extends Array<any>, Ret>(self: T, body: (this: T, ...args: Args) => Ret) => (...args: Args) => Ret
+>    : ^ ^^    ^^^^^^^^^          ^^   ^^    ^^ ^^    ^^                               ^^^^^                      
+>{ message: "foo" } : { message: string; }
+>                   : ^^^^^^^^^^^^^^^^^^^^
+>message : string
+>        : ^^^^^^
+>"foo" : "foo"
+>      : ^^^^^
+>function <N>(n: N) {  this.message;} : <N>(this: { message: string; }, n: N) => void
+>                                     : ^ ^^    ^^^^^^^^^^^^^^^^^^^^^^^^ ^^ ^^^^^^^^^
+>n : N
+>  : ^
+
+  this.message;
+>this.message : string
+>             : ^^^^^^
+>this : { message: string; }
+>     : ^^^^^^^^^^^^^^^^^^^^
+>message : string
+>        : ^^^^^^
+
+});
+
+declare const fn2: <Args extends Array<any>, Ret>(
+>fn2 : <Args extends Array<any>, Ret>(body: (first: string, ...args: Args) => Ret) => (...args: Args) => Ret
+>    : ^    ^^^^^^^^^          ^^   ^^    ^^                                     ^^^^^                      
+
+  body: (first: string, ...args: Args) => Ret,
+>body : (first: string, ...args: Args) => Ret
+>     : ^     ^^      ^^^^^    ^^    ^^^^^   
+>first : string
+>      : ^^^^^^
+>args : Args
+>     : ^^^^
+
+) => (...args: Args) => Ret;
+>args : Args
+>     : ^^^^
+
+export const ok3 = fn2(function <N>(first, n: N) {});
+>ok3 : <N>(n: N) => void
+>    : ^ ^^^^^^^^^^^^^^^
+>fn2(function <N>(first, n: N) {}) : <N>(n: N) => void
+>                                  : ^ ^^^^^^^^^^^^^^^
+>fn2 : <Args extends Array<any>, Ret>(body: (first: string, ...args: Args) => Ret) => (...args: Args) => Ret
+>    : ^    ^^^^^^^^^          ^^   ^^    ^^                                     ^^^^^                      
+>function <N>(first, n: N) {} : <N>(first: string, n: N) => void
+>                             : ^ ^^     ^^^^^^^^^^ ^^ ^^^^^^^^^
+>first : string
+>      : ^^^^^^
+>n : N
+>  : ^
+
+declare const fn3: <Args extends Array<any>, Ret>(
+>fn3 : <Args extends Array<any>, Ret>(body: (...args: Args) => (arg: string) => Ret) => (...args: Args) => Ret
+>    : ^    ^^^^^^^^^          ^^   ^^    ^^                                       ^^^^^                      
+
+  body: (...args: Args) => (arg: string) => Ret,
+>body : (...args: Args) => (arg: string) => Ret
+>     : ^^^^    ^^    ^^^^^                    
+>args : Args
+>     : ^^^^
+>arg : string
+>    : ^^^^^^
+
+) => (...args: Args) => Ret;
+>args : Args
+>     : ^^^^
+
+export const ok4 = fn3(function <N>(n: N) {
+>ok4 : <N>(n: N) => number
+>    : ^ ^^^^^^^^^^^^^^^^^
+>fn3(function <N>(n: N) {    return (arg) => {        return 10    }}) : <N>(n: N) => number
+>                                                                      : ^ ^^^^^^^^^^^^^^^^^
+>fn3 : <Args extends Array<any>, Ret>(body: (...args: Args) => (arg: string) => Ret) => (...args: Args) => Ret
+>    : ^    ^^^^^^^^^          ^^   ^^    ^^                                       ^^^^^                      
+>function <N>(n: N) {    return (arg) => {        return 10    }} : <N>(n: N) => (arg: string) => number
+>                                                                 : ^ ^^ ^^ ^^^^^^   ^^^^^^^^^^^^^^^^^^^
+>n : N
+>  : ^
+
+    return (arg) => {
+>(arg) => {        return 10    } : (arg: string) => number
+>                                 : ^   ^^^^^^^^^^^^^^^^^^^
+>arg : string
+>    : ^^^^^^
+
+        return 10
+>10 : 10
+>   : ^^
+    }
+});
+
+declare function fn4<T, P>(config: {
+>fn4 : <T, P>(config: { context: T; callback: (params: P) => (context: T, params: P) => number; }) => (params: P) => number
+>    : ^ ^^ ^^      ^^                                                                           ^^^^^                     
+>config : { context: T; callback: (params: P) => (context: T, params: P) => number; }
+>       : ^^^^^^^^^^^ ^^^^^^^^^^^^                                                ^^^
+
+  context: T;
+>context : T
+>        : ^
+
+  callback: (params: P) => (context: T, params: P) => number;
+>callback : (params: P) => (context: T, params: P) => number
+>         : ^      ^^ ^^^^^                                 
+>params : P
+>       : ^
+>context : T
+>        : ^
+>params : P
+>       : ^
+
+}): (params: P) => number;
+>params : P
+>       : ^
+
+export const ok5 = fn4({
+>ok5 : (params: T) => number
+>    : ^      ^^^^^^^^      
+>fn4({  context: 1,  callback: <T,>(params: T) => {    return (a, b) => a + 1;  },}) : (params: T) => number
+>                                                                                    : ^      ^^^^^^^^      
+>fn4 : <T, P>(config: { context: T; callback: (params: P) => (context: T, params: P) => number; }) => (params: P) => number
+>    : ^ ^^ ^^      ^^                                                                           ^^^^^                     
+>{  context: 1,  callback: <T,>(params: T) => {    return (a, b) => a + 1;  },} : { context: number; callback: <T>(params: T) => (a: number, b: T) => number; }
+>                                                                               : ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^      ^^ ^^^^^^ ^^^^^^^^^^ ^^^^^^^^^^^^^^^^^
+
+  context: 1,
+>context : number
+>        : ^^^^^^
+>1 : 1
+>  : ^
+
+  callback: <T,>(params: T) => {
+>callback : <T>(params: T) => (a: number, b: T) => number
+>         : ^ ^^      ^^ ^^^^^^ ^^^^^^^^^^ ^^^^^^^^^^^^^^
+><T,>(params: T) => {    return (a, b) => a + 1;  } : <T>(params: T) => (a: number, b: T) => number
+>                                                   : ^ ^^      ^^ ^^^^^^ ^^^^^^^^^^ ^^^^^^^^^^^^^^
+>params : T
+>       : ^
+
+    return (a, b) => a + 1;
+>(a, b) => a + 1 : (a: number, b: T) => number
+>                : ^ ^^^^^^^^^^ ^^^^^^^^^^^^^^
+>a : number
+>  : ^^^^^^
+>b : T
+>  : ^
+>a + 1 : number
+>      : ^^^^^^
+>a : number
+>  : ^^^^^^
+>1 : 1
+>  : ^
+
+  },
+});
+
+declare const fnGen1: <T, Args extends Array<any>, Ret>(
+>fnGen1 : <T, Args extends Array<any>, Ret>(self: T, body: (this: T, ...args: Args) => Generator<any, Ret, never>) => (...args: Args) => Ret
+>       : ^ ^^    ^^^^^^^^^          ^^   ^^    ^^ ^^    ^^                                                      ^^^^^                      
+
+  self: T,
+>self : T
+>     : ^
+
+  body: (this: T, ...args: Args) => Generator<any, Ret, never>,
+>body : (this: T, ...args: Args) => Generator<any, Ret, never>
+>     : ^    ^^ ^^^^^    ^^    ^^^^^                          
+>this : T
+>     : ^
+>args : Args
+>     : ^^^^
+
+) => (...args: Args) => Ret;
+>args : Args
+>     : ^^^^
+
+export const ok6 = fnGen1({ message: "foo" }, function* (n: number) {
+>ok6 : (n: number) => void
+>    : ^^^^^^^^^^^^^^^^^^^
+>fnGen1({ message: "foo" }, function* (n: number) {  this.message;}) : (n: number) => void
+>                                                                    : ^^^^^^^^^^^^^^^^^^^
+>fnGen1 : <T, Args extends Array<any>, Ret>(self: T, body: (this: T, ...args: Args) => Generator<any, Ret, never>) => (...args: Args) => Ret
+>       : ^ ^^    ^^^^^^^^^          ^^   ^^    ^^ ^^    ^^                                                      ^^^^^                      
+>{ message: "foo" } : { message: string; }
+>                   : ^^^^^^^^^^^^^^^^^^^^
+>message : string
+>        : ^^^^^^
+>"foo" : "foo"
+>      : ^^^^^
+>function* (n: number) {  this.message;} : (this: { message: string; }, n: number) => Generator<never, void, never>
+>                                        : ^    ^^^^^^^^^^^^^^^^^^^^^^^^ ^^      ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+>n : number
+>  : ^^^^^^
+
+  this.message;
+>this.message : string
+>             : ^^^^^^
+>this : { message: string; }
+>     : ^^^^^^^^^^^^^^^^^^^^
+>message : string
+>        : ^^^^^^
+
+});
+
+export const ok7 = fnGen1({ message: "foo" }, function* <N>(n: N) {
+>ok7 : (n: any) => void
+>    : ^^^^^^^^^^^^^^^^
+>fnGen1({ message: "foo" }, function* <N>(n: N) {  this.message;}) : (n: any) => void
+>                                                                  : ^^^^^^^^^^^^^^^^
+>fnGen1 : <T, Args extends Array<any>, Ret>(self: T, body: (this: T, ...args: Args) => Generator<any, Ret, never>) => (...args: Args) => Ret
+>       : ^ ^^    ^^^^^^^^^          ^^   ^^    ^^ ^^    ^^                                                      ^^^^^                      
+>{ message: "foo" } : { message: string; }
+>                   : ^^^^^^^^^^^^^^^^^^^^
+>message : string
+>        : ^^^^^^
+>"foo" : "foo"
+>      : ^^^^^
+>function* <N>(n: N) {  this.message;} : <N>(this: { message: string; }, n: N) => Generator<never, void, never>
+>                                      : ^ ^^    ^^^^^^^^^^^^^^^^^^^^^^^^ ^^ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+>n : N
+>  : ^
+
+  this.message;
+>this.message : string
+>             : ^^^^^^
+>this : { message: string; }
+>     : ^^^^^^^^^^^^^^^^^^^^
+>message : string
+>        : ^^^^^^
+
+});
+
diff --git a/tests/cases/compiler/contextualTypingGenericFunction2.ts b/tests/cases/compiler/contextualTypingGenericFunction2.ts
new file mode 100644
index 0000000000000..13a4e42c9baeb
--- /dev/null
+++ b/tests/cases/compiler/contextualTypingGenericFunction2.ts
@@ -0,0 +1,60 @@
+// @strict: true
+// @target: esnext
+// @declaration: true
+// @emitDeclarationOnly: true
+
+// https://github.com/microsoft/TypeScript/issues/61791
+
+declare const fn1: <T, Args extends Array<any>, Ret>(
+  self: T,
+  body: (this: T, ...args: Args) => Ret,
+) => (...args: Args) => Ret;
+
+export const ok1 = fn1({ message: "foo" }, function (n: number) {
+  this.message;
+});
+
+export const ok2 = fn1({ message: "foo" }, function <N>(n: N) {
+  this.message;
+});
+
+declare const fn2: <Args extends Array<any>, Ret>(
+  body: (first: string, ...args: Args) => Ret,
+) => (...args: Args) => Ret;
+
+export const ok3 = fn2(function <N>(first, n: N) {});
+
+declare const fn3: <Args extends Array<any>, Ret>(
+  body: (...args: Args) => (arg: string) => Ret,
+) => (...args: Args) => Ret;
+
+export const ok4 = fn3(function <N>(n: N) {
+    return (arg) => {
+        return 10
+    }
+});
+
+declare function fn4<T, P>(config: {
+  context: T;
+  callback: (params: P) => (context: T, params: P) => number;
+}): (params: P) => number;
+
+export const ok5 = fn4({
+  context: 1,
+  callback: <T,>(params: T) => {
+    return (a, b) => a + 1;
+  },
+});
+
+declare const fnGen1: <T, Args extends Array<any>, Ret>(
+  self: T,
+  body: (this: T, ...args: Args) => Generator<any, Ret, never>,
+) => (...args: Args) => Ret;
+
+export const ok6 = fnGen1({ message: "foo" }, function* (n: number) {
+  this.message;
+});
+
+export const ok7 = fnGen1({ message: "foo" }, function* <N>(n: N) {
+  this.message;
+});
diff --git a/tests/cases/fourslash/contextualTypingGenericFunction1.ts b/tests/cases/fourslash/contextualTypingGenericFunction1.ts
index 9fa6b92da237a..31411f72609c9 100644
--- a/tests/cases/fourslash/contextualTypingGenericFunction1.ts
+++ b/tests/cases/fourslash/contextualTypingGenericFunction1.ts
@@ -1,6 +1,5 @@
 /// <reference path='fourslash.ts'/>
 
-// should not contextually type the RHS because it introduces type parameters
 ////var obj: { f<T>(x: T): T } = { f: <S>(/*1*/x) => x };
 ////var obj2: <T>(x: T) => T = <S>(/*2*/x) => x;
 ////
@@ -11,7 +10,7 @@
 ////c.obj = <S>(/*3*/x) => x;
 
 verify.quickInfos({
-    1: "(parameter) x: any",
-    2: "(parameter) x: any",
-    3: "(parameter) x: any"
+    1: "(parameter) x: T",
+    2: "(parameter) x: T",
+    3: "(parameter) x: T"
 });