diff --git a/Lib/asyncio/timeouts.py b/Lib/asyncio/timeouts.py
index 029c468739bf2d..826201b8b06e34 100644
--- a/Lib/asyncio/timeouts.py
+++ b/Lib/asyncio/timeouts.py
@@ -84,9 +84,9 @@ def __repr__(self) -> str:
     async def __aenter__(self) -> "Timeout":
         self._state = _State.ENTERED
         self._task = tasks.current_task()
-        self._cancelling = self._task.cancelling()
         if self._task is None:
             raise RuntimeError("Timeout should be used inside a task")
+        self._cancelling = self._task.cancelling()
         self.reschedule(self._when)
         return self
 
diff --git a/Misc/ACKS b/Misc/ACKS
index 94cb1965676f48..3783f511bb7240 100644
--- a/Misc/ACKS
+++ b/Misc/ACKS
@@ -760,6 +760,7 @@ Aaron Hill
 Joel Hillacre
 Richie Hindle
 Konrad Hinsen
+James Hilton-Balfe
 Richard Hoberecht
 David Hobley
 Tim Hochberg
diff --git a/Misc/NEWS.d/next/Library/2023-10-19-11-40-38.gh-issue-111085.hBPpQr.rst b/Misc/NEWS.d/next/Library/2023-10-19-11-40-38.gh-issue-111085.hBPpQr.rst
new file mode 100644
index 00000000000000..ff4229dae8480a
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2023-10-19-11-40-38.gh-issue-111085.hBPpQr.rst
@@ -0,0 +1 @@
+Fix :class:`asyncio.Timeout` raising an :exc:`AttributeError` over a :exc:`RuntimeError` due to logic bug. Patch by James Hilton-Balfe