diff --git a/news/7390.trivial.rst b/news/7390.trivial.rst
new file mode 100644
index 00000000000..788c67a7293
--- /dev/null
+++ b/news/7390.trivial.rst
@@ -0,0 +1 @@
+Enhance the log message while downloading a pip file
\ No newline at end of file
diff --git a/src/pip/_internal/network/download.py b/src/pip/_internal/network/download.py
index 47af547d6fc..1fa9f857ccb 100644
--- a/src/pip/_internal/network/download.py
+++ b/src/pip/_internal/network/download.py
@@ -10,7 +10,6 @@
 
 from pip._internal.cli.progress_bars import DownloadProgressProvider
 from pip._internal.exceptions import NetworkConnectionError
-from pip._internal.models.index import PyPI
 from pip._internal.models.link import Link
 from pip._internal.network.cache import is_from_cache
 from pip._internal.network.session import PipSession
@@ -34,11 +33,7 @@ def _prepare_download(
 ) -> Iterable[bytes]:
     total_length = _get_http_response_size(resp)
 
-    if link.netloc == PyPI.file_storage_domain:
-        url = link.show_url
-    else:
-        url = link.url_without_fragment
-
+    url = link.show_url
     logged_url = redact_auth_from_url(url)
 
     if total_length:
diff --git a/tests/unit/test_network_download.py b/tests/unit/test_network_download.py
index 20f5513a2df..357bb0b2a66 100644
--- a/tests/unit/test_network_download.py
+++ b/tests/unit/test_network_download.py
@@ -14,17 +14,17 @@
 
 @pytest.mark.parametrize("url, headers, from_cache, expected", [
     ('http://example.com/foo.tgz', {}, False,
-        "Downloading http://example.com/foo.tgz"),
+        "Downloading foo.tgz"),
     ('http://example.com/foo.tgz', {'content-length': 2}, False,
-        "Downloading http://example.com/foo.tgz (2 bytes)"),
+        "Downloading foo.tgz (2 bytes)"),
     ('http://example.com/foo.tgz', {'content-length': 2}, True,
-        "Using cached http://example.com/foo.tgz (2 bytes)"),
+        "Using cached foo.tgz (2 bytes)"),
     ('https://files.pythonhosted.org/foo.tgz', {}, False,
         "Downloading foo.tgz"),
     ('https://files.pythonhosted.org/foo.tgz', {'content-length': 2}, False,
         "Downloading foo.tgz (2 bytes)"),
     ('https://files.pythonhosted.org/foo.tgz', {'content-length': 2}, True,
-        "Using cached foo.tgz"),
+        "Using cached foo.tgz (2 bytes)"),
 ])
 def test_prepare_download__log(caplog, url, headers, from_cache, expected):
     caplog.set_level(logging.INFO)