diff --git a/Lib/asyncio/sslproto.py b/Lib/asyncio/sslproto.py
index 367f7d07a4184a..79e0745a75256a 100644
--- a/Lib/asyncio/sslproto.py
+++ b/Lib/asyncio/sslproto.py
@@ -478,7 +478,11 @@ def connection_lost(self, exc):
             self._loop.call_soon(self._app_protocol.connection_lost, exc)
         self._transport = None
         self._app_transport = None
+        if getattr(self, '_handshake_timeout_handle', None):
+            self._handshake_timeout_handle.cancel()
         self._wakeup_waiter(exc)
+        self._app_protocol = None
+        self._sslpipe = None
 
     def pause_writing(self):
         """Called when the low-level transport's buffer goes over
diff --git a/Misc/NEWS.d/next/Library/2019-03-17-16-43-29.bpo-34745.nOfm7_.rst b/Misc/NEWS.d/next/Library/2019-03-17-16-43-29.bpo-34745.nOfm7_.rst
new file mode 100644
index 00000000000000..d88f36a6d21736
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-03-17-16-43-29.bpo-34745.nOfm7_.rst
@@ -0,0 +1 @@
+Fix :mod:`asyncio` ssl memory issues caused by circular references