diff --git a/Lib/unittest/mock.py b/Lib/unittest/mock.py
index 34f2dd77ec6..66ace80cb5f 100644
--- a/Lib/unittest/mock.py
+++ b/Lib/unittest/mock.py
@@ -48,6 +48,8 @@ _safe_super = super
 def _is_async_obj(obj):
     if _is_instance_mock(obj) and not isinstance(obj, AsyncMock):
         return False
+    if hasattr(obj, '__func__'):
+        obj = getattr(obj, '__func__')
     return asyncio.iscoroutinefunction(obj) or inspect.isawaitable(obj)
 
 
diff --git a/Lib/unittest/test/testmock/testasync.py b/Lib/unittest/test/testmock/testasync.py
index 0bd7ae4929c..e68022afdcc 100644
--- a/Lib/unittest/test/testmock/testasync.py
+++ b/Lib/unittest/test/testmock/testasync.py
@@ -19,6 +19,15 @@ class AsyncClass:
     def normal_method(self):
         pass
 
+    @classmethod
+    async def async_class_method(cls):
+        pass
+
+    @staticmethod
+    async def async_static_method():
+        pass
+
+
 class AwaitableClass:
     def __await__(self):
         yield
@@ -71,6 +80,20 @@ class AsyncPatchDecoratorTest(unittest.TestCase):
 
         test_async()
 
+    def test_is_AsyncMock_patch_staticmethod(self):
+        @patch.object(AsyncClass, 'async_static_method')
+        def test_async(mock_method):
+            self.assertIsInstance(mock_method, AsyncMock)
+
+        test_async()
+
+    def test_is_AsyncMock_patch_classmethod(self):
+        @patch.object(AsyncClass, 'async_class_method')
+        def test_async(mock_method):
+            self.assertIsInstance(mock_method, AsyncMock)
+
+        test_async()
+
     def test_async_def_patch(self):
         @patch(f"{__name__}.async_func", return_value=1)
         @patch(f"{__name__}.async_func_args", return_value=2)
diff --git a/Misc/NEWS.d/next/Library/2020-01-24-13-24-35.bpo-39082.qKgrq_.rst b/Misc/NEWS.d/next/Library/2020-01-24-13-24-35.bpo-39082.qKgrq_.rst
new file mode 100644
index 00000000000..52c4ee1b33b
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2020-01-24-13-24-35.bpo-39082.qKgrq_.rst
@@ -0,0 +1 @@
+Allow AsyncMock to correctly patch static/class methods