diff --git a/django/contrib/sitemaps/__init__.py b/django/contrib/sitemaps/__init__.py
index 13e667e142..2d0e047233 100644
--- a/django/contrib/sitemaps/__init__.py
+++ b/django/contrib/sitemaps/__init__.py
@@ -54,9 +54,9 @@ class Sitemap:
         return obj.get_absolute_url()
 
     def _get_paginator(self):
-        if not hasattr(self, "paginator"):
-            self.paginator = paginator.Paginator(self.items(), self.limit)
-        return self.paginator
+        if not hasattr(self, "_paginator"):
+            self._paginator = paginator.Paginator(self.items(), self.limit)
+        return self._paginator
     paginator = property(_get_paginator)
 
     def get_urls(self, page=1):