diff --git a/news/13358.bugfix.rst b/news/13358.bugfix.rst
new file mode 100644
index 00000000000..e2c6fbe02da
--- /dev/null
+++ b/news/13358.bugfix.rst
@@ -0,0 +1 @@
+Automatically use the legacy (non-PEP517) mode even without the ``wheel`` package.
diff --git a/src/pip/_internal/pyproject.py b/src/pip/_internal/pyproject.py
index 0e8452f39dc..d319b483b7f 100644
--- a/src/pip/_internal/pyproject.py
+++ b/src/pip/_internal/pyproject.py
@@ -105,11 +105,7 @@ def load_pyproject_toml(
     # https://discuss.python.org/t/pip-without-setuptools-could-the-experience-be-improved/11810/9
     # https://github.com/pypa/pip/issues/8559
     elif use_pep517 is None:
-        use_pep517 = (
-            has_pyproject
-            or not importlib.util.find_spec("setuptools")
-            or not importlib.util.find_spec("wheel")
-        )
+        use_pep517 = has_pyproject or not importlib.util.find_spec("setuptools")
 
     # At this point, we know whether we're going to use PEP 517.
     assert use_pep517 is not None