diff --git a/django/db/models/fields/related.py b/django/db/models/fields/related.py
index f1bc664007dd..332a168a7844 100644
--- a/django/db/models/fields/related.py
+++ b/django/db/models/fields/related.py
@@ -348,6 +348,24 @@ def _check_clashes(self):
                     )
                 )
 
+        # Check clash between reverse accessor and manager names on
+        # the target model.
+        if not rel_is_hidden:
+            manager_names = {m.name for m in rel_opts.managers}
+            if rel_name in manager_names:
+                errors.append(
+                    checks.Error(
+                        f"Related name '{rel_name}' for '{field_name}' "
+                        f"clashes with the name of a model manager.",
+                        hint=(
+                            "Rename the model manager or change the related_name "
+                            "argument in the definition for field '%s'." % field_name
+                        ),
+                        obj=self,
+                        id="fields.E348",
+                    )
+                )
+
         return errors
 
     def db_type(self, connection):
@@ -589,7 +607,6 @@ def check(self, **kwargs):
             *self._check_to_fields_exist(),
             *self._check_to_fields_composite_pk(),
             *self._check_unique_target(),
-            *self._check_conflict_with_managers(),
         ]
 
     def _check_to_fields_exist(self):
@@ -719,27 +736,6 @@ def _check_unique_target(self):
                 ]
         return []
 
-    def _check_conflict_with_managers(self):
-        errors = []
-        manager_names = {manager.name for manager in self.opts.managers}
-        for rel_objs in self.model._meta.related_objects:
-            related_object_name = rel_objs.name
-            if related_object_name in manager_names:
-                field_name = f"{self.model._meta.object_name}.{self.name}"
-                errors.append(
-                    checks.Error(
-                        f"Related name '{related_object_name}' for '{field_name}' "
-                        "clashes with the name of a model manager.",
-                        hint=(
-                            "Rename the model manager or change the related_name "
-                            f"argument in the definition for field '{field_name}'."
-                        ),
-                        obj=self,
-                        id="fields.E348",
-                    )
-                )
-        return errors
-
     def deconstruct(self):
         name, path, args, kwargs = super().deconstruct()
         kwargs["on_delete"] = self.remote_field.on_delete
diff --git a/docs/releases/6.0.4.txt b/docs/releases/6.0.4.txt
index 1967edacc840..de75dc7d1332 100644
--- a/docs/releases/6.0.4.txt
+++ b/docs/releases/6.0.4.txt
@@ -18,3 +18,8 @@ Bugfixes
 * Fixed a regression in Django 6.0 in admin forms where
   ``RelatedFieldWidgetWrapper`` incorrectly wrapped all widgets in a
   ``<fieldset>`` (:ticket:`36949`).
+
+* Fixed a bug in Django 6.0 where the ``fields.E348`` system check did not
+  detect name clashes between model managers and
+  :attr:`~django.db.models.ForeignKey.related_name`\s for non-self-referential
+  relationships (:ticket:`36973`).
diff --git a/tests/invalid_models_tests/test_relative_fields.py b/tests/invalid_models_tests/test_relative_fields.py
index 51b1de149427..a6edcc4e048e 100644
--- a/tests/invalid_models_tests/test_relative_fields.py
+++ b/tests/invalid_models_tests/test_relative_fields.py
@@ -1579,11 +1579,12 @@ class Author(models.Model):
             Author.check(),
             [
                 Error(
-                    "Related name 'authors' for 'Author.mentor' clashes with the name "
-                    "of a model manager.",
+                    "Related name 'authors' for 'invalid_models_tests.Author.mentor' "
+                    "clashes with the name of a model manager.",
                     hint=(
                         "Rename the model manager or change the related_name argument "
-                        "in the definition for field 'Author.mentor'."
+                        "in the definition for field "
+                        "'invalid_models_tests.Author.mentor'."
                     ),
                     obj=Author._meta.get_field("mentor"),
                     id="fields.E348",
@@ -1591,6 +1592,31 @@ class Author(models.Model):
             ],
         )
 
+    def test_clash_between_rel_name_and_manager_non_self_referential(self):
+        class Thing(models.Model):
+            items = models.Manager()
+
+        class Item(models.Model):
+            thing = models.ForeignKey(Thing, models.CASCADE, related_name="items")
+            something = models.ForeignKey(Thing, models.CASCADE, related_name="+")
+
+        self.assertEqual(
+            Item.check(),
+            [
+                Error(
+                    "Related name 'items' for 'invalid_models_tests.Item.thing' "
+                    "clashes with the name of a model manager.",
+                    hint=(
+                        "Rename the model manager or change the related_name argument "
+                        "in the definition for field 'invalid_models_tests.Item.thing'."
+                    ),
+                    obj=Item._meta.get_field("thing"),
+                    id="fields.E348",
+                )
+            ],
+        )
+        self.assertEqual(Thing.check(), [])
+
 
 @isolate_apps("invalid_models_tests")
 class SelfReferentialM2MClashTests(SimpleTestCase):