diff --git a/news/4962.bugfix b/news/4962.bugfix
new file mode 100644
index 00000000000..c3e9a494cd4
--- /dev/null
+++ b/news/4962.bugfix
@@ -0,0 +1 @@
+Detect x32 userspace ABI on 64-bit kernel
diff --git a/src/pip/_internal/pep425tags.py b/src/pip/_internal/pep425tags.py
index 0b5c7832d4f..1bb5aabdbd4 100644
--- a/src/pip/_internal/pep425tags.py
+++ b/src/pip/_internal/pep425tags.py
@@ -135,7 +135,12 @@ def get_platform():
     if result == "linux_x86_64" and _is_running_32bit():
         # 32 bit Python program (running on a 64 bit Linux): pip should only
         # install and run 32 bit compiled extensions in that case.
-        result = "linux_i686"
+        machine = platform.machine()
+
+        if machine == "x86_64":
+            result = "linux_x32"
+        else:
+            result = "linux_i686"  # and machine == "i686"
 
     return result