diff --git a/doc/api/next_api_changes/deprecations/20209-AL.rst b/doc/api/next_api_changes/deprecations/20209-AL.rst
new file mode 100644
index 000000000000..79c462cd048f
--- /dev/null
+++ b/doc/api/next_api_changes/deprecations/20209-AL.rst
@@ -0,0 +1,3 @@
+``cbook.report_memory``
+~~~~~~~~~~~~~~~~~~~~~~~
+... is deprecated.  Use ``psutil.virtual_memory`` instead.
diff --git a/lib/matplotlib/cbook/__init__.py b/lib/matplotlib/cbook/__init__.py
index 3e0d0062dd03..c8070e2b4ec8 100644
--- a/lib/matplotlib/cbook/__init__.py
+++ b/lib/matplotlib/cbook/__init__.py
@@ -628,6 +628,7 @@ def remove(self, o):
                 self.push(elem)
 
 
+@_api.deprecated("3.5", alternative="psutil.virtual_memory")
 def report_memory(i=0):  # argument may go away
     """Return the memory consumed by the process."""
     def call(command, os_name):