diff --git a/src/_pytest/assertion/__init__.py b/src/_pytest/assertion/__init__.py
index cdb034703..0a57f6afa 100644
--- a/src/_pytest/assertion/__init__.py
+++ b/src/_pytest/assertion/__init__.py
@@ -7,6 +7,7 @@ from typing import Optional
 from _pytest.assertion import rewrite
 from _pytest.assertion import truncate
 from _pytest.assertion import util
+from _pytest.assertion.rewrite import assertstate_key
 from _pytest.compat import TYPE_CHECKING
 from _pytest.config import hookimpl
 
@@ -82,13 +83,13 @@ class AssertionState:
 
 def install_importhook(config):
     """Try to install the rewrite hook, raise SystemError if it fails."""
-    config._assertstate = AssertionState(config, "rewrite")
-    config._assertstate.hook = hook = rewrite.AssertionRewritingHook(config)
+    config._store[assertstate_key] = AssertionState(config, "rewrite")
+    config._store[assertstate_key].hook = hook = rewrite.AssertionRewritingHook(config)
     sys.meta_path.insert(0, hook)
-    config._assertstate.trace("installed rewrite import hook")
+    config._store[assertstate_key].trace("installed rewrite import hook")
 
     def undo():
-        hook = config._assertstate.hook
+        hook = config._store[assertstate_key].hook
         if hook is not None and hook in sys.meta_path:
             sys.meta_path.remove(hook)
 
@@ -100,7 +101,7 @@ def pytest_collection(session: "Session") -> None:
     # this hook is only called when test modules are collected
     # so for example not in the master process of pytest-xdist
     # (which does not collect test modules)
-    assertstate = getattr(session.config, "_assertstate", None)
+    assertstate = session.config._store.get(assertstate_key, None)
     if assertstate:
         if assertstate.hook is not None:
             assertstate.hook.set_session(session)
@@ -163,7 +164,7 @@ def pytest_runtest_protocol(item):
 
 
 def pytest_sessionfinish(session):
-    assertstate = getattr(session.config, "_assertstate", None)
+    assertstate = session.config._store.get(assertstate_key, None)
     if assertstate:
         if assertstate.hook is not None:
             assertstate.hook.set_session(None)
diff --git a/src/_pytest/assertion/rewrite.py b/src/_pytest/assertion/rewrite.py
index 00bdcfc3e..f84127dca 100644
--- a/src/_pytest/assertion/rewrite.py
+++ b/src/_pytest/assertion/rewrite.py
@@ -26,9 +26,18 @@ from _pytest.assertion.util import (  # noqa: F401
     format_explanation as _format_explanation,
 )
 from _pytest.compat import fspath
+from _pytest.compat import TYPE_CHECKING
 from _pytest.pathlib import fnmatch_ex
 from _pytest.pathlib import Path
 from _pytest.pathlib import PurePath
+from _pytest.store import StoreKey
+
+if TYPE_CHECKING:
+    from _pytest.assertion import AssertionState  # noqa: F401
+
+
+assertstate_key = StoreKey["AssertionState"]()
+
 
 # pytest caches rewritten pycs in pycache dirs
 PYTEST_TAG = "{}-pytest-{}".format(sys.implementation.cache_tag, version)
@@ -65,7 +74,7 @@ class AssertionRewritingHook(importlib.abc.MetaPathFinder, importlib.abc.Loader)
     def find_spec(self, name, path=None, target=None):
         if self._writing_pyc:
             return None
-        state = self.config._assertstate
+        state = self.config._store[assertstate_key]
         if self._early_rewrite_bailout(name, state):
             return None
         state.trace("find_module called for: %s" % name)
@@ -104,7 +113,7 @@ class AssertionRewritingHook(importlib.abc.MetaPathFinder, importlib.abc.Loader)
 
     def exec_module(self, module):
         fn = Path(module.__spec__.origin)
-        state = self.config._assertstate
+        state = self.config._store[assertstate_key]
 
         self._rewritten_names.add(module.__name__)