diff --git a/fsspec/implementations/http.py b/fsspec/implementations/http.py
index ad7f63916..d766df590 100644
--- a/fsspec/implementations/http.py
+++ b/fsspec/implementations/http.py
@@ -123,9 +123,10 @@ def close_session(loop, session):
                 return
             except (TimeoutError, FSTimeoutError):
                 pass
-        if session._connector is not None:
+        connector = getattr(session, "_connector", None)
+        if connector is not None:
             # close after loop is dead
-            session._connector._close()
+            connector._close()
 
     async def set_session(self):
         if self._session is None:
diff --git a/fsspec/implementations/tests/test_http.py b/fsspec/implementations/tests/test_http.py
index ec9e02fc6..dfa89c3f8 100644
--- a/fsspec/implementations/tests/test_http.py
+++ b/fsspec/implementations/tests/test_http.py
@@ -475,6 +475,19 @@ def test_put_file(server, tmp_path, method, reset_files):
     assert fs.cat(server + "/hey_3") == b"yyy"
 
 
+async def get_aiohttp():
+    from aiohttp import ClientSession
+
+    return ClientSession()
+
+
+async def get_proxy():
+    class ProxyClient:
+        pass
+
+    return ProxyClient()
+
+
 @pytest.mark.xfail(
     condition=sys.flags.optimize > 1, reason="no docstrings when optimised"
 )
@@ -548,3 +561,10 @@ def test_processes(server, method):
     out = q.get()
     assert out == fs.cat(fn)
     p.join()
+
+
+@pytest.mark.parametrize("get_client", [get_aiohttp, get_proxy])
+@pytest.mark.skipif(sys.version_info < (3, 7), reason="no asyncio.run in <3.7")
+def test_close(get_client):
+    fs = fsspec.filesystem("http", skip_instance_cache=True)
+    fs.close_session(None, asyncio.run(get_client()))