diff --git a/google/auth/transport/_aiohttp_requests.py b/google/auth/transport/_aiohttp_requests.py
index 4293810..ab7dfef 100644
--- a/google/auth/transport/_aiohttp_requests.py
+++ b/google/auth/transport/_aiohttp_requests.py
@@ -138,7 +138,12 @@
     """
 
     def __init__(self, session=None):
-        self.session = None
+        # TODO: Use auto_decompress property for aiohttp 3.7+
+        if session is not None and session._auto_decompress:
+            raise ValueError(
+                "Client sessions with auto_decompress=True are not supported."
+            )
+        self.session = session
 
     async def __call__(
         self,
diff --git a/system_tests/system_tests_async/conftest.py b/system_tests/system_tests_async/conftest.py
index 47a473e..9669099 100644
--- a/system_tests/system_tests_async/conftest.py
+++ b/system_tests/system_tests_async/conftest.py
@@ -26,9 +26,7 @@
 from google.auth.transport import _aiohttp_requests as aiohttp_requests
 from system_tests.system_tests_sync import conftest as sync_conftest
 
-ASYNC_REQUESTS_SESSION = aiohttp.ClientSession()
 
-ASYNC_REQUESTS_SESSION.verify = False
 TOKEN_INFO_URL = "https://www.googleapis.com/oauth2/v3/tokeninfo"
 
 
@@ -49,10 +47,18 @@
     """The full path to a valid authorized user file."""
     yield sync_conftest.AUTHORIZED_USER_FILE
 
+
+@pytest.fixture
+async def aiohttp_session():
+    async with aiohttp.ClientSession(auto_decompress=False) as session:
+        yield session
+
+
 @pytest.fixture(params=["aiohttp"])
-async def http_request(request):
+async def http_request(request, aiohttp_session):
     """A transport.request object."""
-    yield aiohttp_requests.Request(ASYNC_REQUESTS_SESSION)
+    yield aiohttp_requests.Request(aiohttp_session)
+
 
 @pytest.fixture
 async def token_info(http_request):
diff --git a/tests_async/transport/test_aiohttp_requests.py b/tests_async/transport/test_aiohttp_requests.py
index 10c31db..a64a4ee 100644
--- a/tests_async/transport/test_aiohttp_requests.py
+++ b/tests_async/transport/test_aiohttp_requests.py
@@ -112,11 +112,18 @@
         return aiohttp_requests.Request()
 
     def make_with_parameter_request(self):
-        http = mock.create_autospec(aiohttp.ClientSession, instance=True)
+        http = aiohttp.ClientSession(auto_decompress=False)
         return aiohttp_requests.Request(http)
 
+    def test_unsupported_session(self):
+        http = aiohttp.ClientSession(auto_decompress=True)
+        with pytest.raises(ValueError):
+            aiohttp_requests.Request(http)
+
     def test_timeout(self):
-        http = mock.create_autospec(aiohttp.ClientSession, instance=True)
+        http = mock.create_autospec(
+            aiohttp.ClientSession, instance=True, _auto_decompress=False
+        )
         request = aiohttp_requests.Request(http)
         request(url="http://example.com", method="GET", timeout=5)
 
@@ -142,7 +149,9 @@
         assert authed_session.credentials == mock.sentinel.credentials
 
     def test_constructor_with_auth_request(self):
-        http = mock.create_autospec(aiohttp.ClientSession)
+        http = mock.create_autospec(
+            aiohttp.ClientSession, instance=True, _auto_decompress=False
+        )
         auth_request = aiohttp_requests.Request(http)
 
         authed_session = aiohttp_requests.AuthorizedSession(