diff --git a/Lib/asyncio/sslproto.py b/Lib/asyncio/sslproto.py
index 488e17d8bccd5b..1966cd7a9f59e3 100644
--- a/Lib/asyncio/sslproto.py
+++ b/Lib/asyncio/sslproto.py
@@ -243,13 +243,12 @@ def abort(self):
         The protocol's connection_lost() method will (eventually) be
         called with None as its argument.
         """
-        self._closed = True
-        if self._ssl_protocol is not None:
-            self._ssl_protocol._abort()
+        self._force_close(None)
 
     def _force_close(self, exc):
         self._closed = True
-        self._ssl_protocol._abort(exc)
+        if self._ssl_protocol is not None:
+            self._ssl_protocol._abort(exc)
 
     def _test__append_write_backlog(self, data):
         # for test only
@@ -614,7 +613,7 @@ def _start_shutdown(self):
         if self._app_transport is not None:
             self._app_transport._closed = True
         if self._state == SSLProtocolState.DO_HANDSHAKE:
-            self._abort()
+            self._abort(None)
         else:
             self._set_state(SSLProtocolState.FLUSHING)
             self._shutdown_timeout_handle = self._loop.call_later(
@@ -661,10 +660,10 @@ def _on_shutdown_complete(self, shutdown_exc):
         else:
             self._loop.call_soon(self._transport.close)
 
-    def _abort(self):
+    def _abort(self, exc):
         self._set_state(SSLProtocolState.UNWRAPPED)
         if self._transport is not None:
-            self._transport.abort()
+            self._transport._force_close(exc)
 
     # Outgoing flow
 
diff --git a/Lib/test/test_asyncio/test_sslproto.py b/Lib/test/test_asyncio/test_sslproto.py
index 37d015339761c6..f5f0afeab51c9e 100644
--- a/Lib/test/test_asyncio/test_sslproto.py
+++ b/Lib/test/test_asyncio/test_sslproto.py
@@ -47,6 +47,7 @@ def connection_made(self, ssl_proto, *, do_handshake=None):
         sslobj = mock.Mock()
         # emulate reading decompressed data
         sslobj.read.side_effect = ssl.SSLWantReadError
+        sslobj.write.side_effect = ssl.SSLWantReadError
         if do_handshake is not None:
             sslobj.do_handshake = do_handshake
         ssl_proto._sslobj = sslobj
@@ -120,7 +121,19 @@ def test_close_during_handshake(self):
         test_utils.run_briefly(self.loop)
 
         ssl_proto._app_transport.close()
-        self.assertTrue(transport.abort.called)
+        self.assertTrue(transport._force_close.called)
+
+    def test_close_during_ssl_over_ssl(self):
+        # gh-113214: passing exceptions from the inner wrapped SSL protocol to the
+        # shim transport provided by the outer SSL protocol should not raise
+        # attribute errors
+        outer = self.ssl_protocol(proto=self.ssl_protocol())
+        self.connection_made(outer)
+        # Closing the outer app transport should not raise an exception
+        messages = []
+        self.loop.set_exception_handler(lambda loop, ctx: messages.append(ctx))
+        outer._app_transport.close()
+        self.assertEqual(messages, [])
 
     def test_get_extra_info_on_closed_connection(self):
         waiter = self.loop.create_future()
diff --git a/Misc/NEWS.d/next/Library/2023-12-20-21-18-51.gh-issue-113214.JcV9Mn.rst b/Misc/NEWS.d/next/Library/2023-12-20-21-18-51.gh-issue-113214.JcV9Mn.rst
new file mode 100644
index 00000000000000..6db74cda166e92
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2023-12-20-21-18-51.gh-issue-113214.JcV9Mn.rst
@@ -0,0 +1 @@
+Fix an ``AttributeError`` during asyncio SSL protocol aborts in SSL-over-SSL scenarios.