diff --git a/src/neo4j/_async/driver.py b/src/neo4j/_async/driver.py
index b60440ef4..1045d7da3 100644
--- a/src/neo4j/_async/driver.py
+++ b/src/neo4j/_async/driver.py
@@ -18,6 +18,7 @@
 
 from __future__ import annotations
 
+import asyncio
 import typing as t
 
 
@@ -466,7 +467,11 @@ def session(self, **config) -> AsyncSession:
     async def close(self) -> None:
         """ Shut down, closing any open connections in the pool.
         """
-        await self._pool.close()
+        try:
+            await self._pool.close()
+        except asyncio.CancelledError:
+            self._closed = True
+            raise
         self._closed = True
 
     if t.TYPE_CHECKING:
diff --git a/src/neo4j/_sync/driver.py b/src/neo4j/_sync/driver.py
index 5aace35b7..7ad02ef7d 100644
--- a/src/neo4j/_sync/driver.py
+++ b/src/neo4j/_sync/driver.py
@@ -18,6 +18,7 @@
 
 from __future__ import annotations
 
+import asyncio
 import typing as t
 
 
@@ -463,7 +464,11 @@ def session(self, **config) -> Session:
     def close(self) -> None:
         """ Shut down, closing any open connections in the pool.
         """
-        self._pool.close()
+        try:
+            self._pool.close()
+        except asyncio.CancelledError:
+            self._closed = True
+            raise
         self._closed = True
 
     if t.TYPE_CHECKING:
diff --git a/tests/integration/mixed/test_async_driver.py b/tests/integration/mixed/test_async_driver.py
index 8e2571cbc..5f71700a6 100644
--- a/tests/integration/mixed/test_async_driver.py
+++ b/tests/integration/mixed/test_async_driver.py
@@ -24,6 +24,7 @@
 import neo4j
 
 from ... import env
+from ..._async_compat import mark_async_test
 
 
 # TODO: Python 3.9: when support gets dropped, remove this mark
@@ -44,7 +45,7 @@ def test_can_create_async_driver_outside_of_loop(uri, auth):
 
     async def return_1(tx: neo4j.AsyncManagedTransaction) -> None:
         nonlocal counter, was_full
-        res = await tx.run("RETURN 1")
+        res = await tx.run("UNWIND range(1, 10000) AS x RETURN x")
 
         counter += 1
         while not was_full and counter < pool_size:
@@ -86,3 +87,55 @@ async def run(driver_: neo4j.AsyncDriver):
         loop.run_until_complete(coro)
     finally:
         loop.close()
+
+
+@mark_async_test
+async def test_cancel_driver_close(uri, auth):
+    class Signal:
+        queried = False
+        released = False
+
+    async def fill_pool(driver_: neo4j.AsyncDriver, n=10):
+        signals = [Signal() for _ in range(n)]
+        await asyncio.gather(
+            *(handle_session(driver_.session(), signals[i]) for i in range(n)),
+            handle_signals(signals),
+            return_exceptions=True,
+        )
+
+    async def handle_signals(signals):
+        while any(not signal.queried for signal in signals):
+            await asyncio.sleep(0.001)
+        await asyncio.sleep(0.1)
+        for signal in signals:
+            signal.released = True
+
+    async def handle_session(session, signal):
+        async with session:
+            await session.execute_read(work, signal)
+
+    async def work(tx: neo4j.AsyncManagedTransaction, signal: Signal) -> None:
+        res = await tx.run("UNWIND range(1, 10000) AS x RETURN x")
+        signal.queried = True
+        while not signal.released:
+            await asyncio.sleep(0.001)
+        await res.consume()
+
+    def connection_count(driver_):
+        return sum(len(v) for v in driver_._pool.connections.values())
+
+    driver = neo4j.AsyncGraphDatabase.driver(uri, auth=auth)
+    await fill_pool(driver)
+    # sanity check, there should be some connections
+    assert connection_count(driver) >= 10
+
+    # start the close and give it some event loop iterations to kick off
+    fut = asyncio.ensure_future(driver.close())
+    await asyncio.sleep(0)
+
+    # cancel in the middle of closing connections
+    fut.cancel()
+    # give the driver a chance to close connections forcefully
+    await asyncio.sleep(0)
+    # driver should be marked as closed to not emmit a ResourceWarning later
+    assert driver._closed == True