diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index fcf576efb73ab..69aeb41a1c04f 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -5058,7 +5058,7 @@ def get_value(self, series: Series, key):
             # try that
             loc = self.get_loc(key)
         except KeyError:
-            if not self._should_fallback_to_positional():
+            if not self._should_fallback_to_positional:
                 raise
             elif is_integer(key):
                 # If the Index cannot hold integer, then this is unambiguously
@@ -5075,6 +5075,7 @@ def _check_indexing_error(self, key):
             # would convert to numpy arrays and raise later any way) - GH29926
             raise InvalidIndexError(key)
 
+    @cache_readonly
     def _should_fallback_to_positional(self) -> bool:
         """
         Should an integer key be treated as positional?
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index 7c4a2e31b96d1..f77236091b09b 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -743,6 +743,7 @@ def _convert_slice_indexer(self, key: slice, kind: str):
 
         return super()._convert_slice_indexer(key, kind)
 
+    @cache_readonly
     def _should_fallback_to_positional(self) -> bool:
         # integer lookups in Series.__getitem__ are unambiguously
         #  positional in this case
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 0876847aed84f..2d5e37e79389e 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -2554,12 +2554,13 @@ def _check_indexing_error(self, key):
             # We have to explicitly exclude generators, as these are hashable.
             raise InvalidIndexError(key)
 
+    @cache_readonly
     def _should_fallback_to_positional(self) -> bool:
         """
         Should integer key(s) be treated as positional?
         """
         # GH#33355
-        return self.levels[0]._should_fallback_to_positional()
+        return self.levels[0]._should_fallback_to_positional
 
     def _get_values_for_loc(self, series: Series, loc, key):
         """
diff --git a/pandas/core/indexes/numeric.py b/pandas/core/indexes/numeric.py
index ea2d5d9eec6ac..fd4259c7037e9 100644
--- a/pandas/core/indexes/numeric.py
+++ b/pandas/core/indexes/numeric.py
@@ -228,6 +228,7 @@ def astype(self, dtype, copy=True):
     # ----------------------------------------------------------------
     # Indexing Methods
 
+    @cache_readonly
     @doc(Index._should_fallback_to_positional)
     def _should_fallback_to_positional(self) -> bool:
         return False
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 59ea6710ea6cd..99ae177aaae6c 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -938,7 +938,7 @@ def __getitem__(self, key):
         if isinstance(key, (list, tuple)):
             key = unpack_1tuple(key)
 
-        if is_integer(key) and self.index._should_fallback_to_positional():
+        if is_integer(key) and self.index._should_fallback_to_positional:
             return self._values[key]
 
         elif key_is_scalar:
@@ -1000,7 +1000,7 @@ def _get_with(self, key):
         if key_type == "integer":
             # We need to decide whether to treat this as a positional indexer
             #  (i.e. self.iloc) or label-based (i.e. self.loc)
-            if not self.index._should_fallback_to_positional():
+            if not self.index._should_fallback_to_positional:
                 return self.loc[key]
             else:
                 return self.iloc[key]
@@ -1122,7 +1122,7 @@ def _set_with(self, key, value):
             # Note: key_type == "boolean" should not occur because that
             #  should be caught by the is_bool_indexer check in __setitem__
             if key_type == "integer":
-                if not self.index._should_fallback_to_positional():
+                if not self.index._should_fallback_to_positional:
                     self._set_labels(key, value)
                 else:
                     self._set_values(key, value)
diff --git a/pandas/tests/indexing/multiindex/test_partial.py b/pandas/tests/indexing/multiindex/test_partial.py
index a99f09143e282..50a31f2fd22c6 100644
--- a/pandas/tests/indexing/multiindex/test_partial.py
+++ b/pandas/tests/indexing/multiindex/test_partial.py
@@ -158,8 +158,8 @@ def test_getitem_intkey_leading_level(
             assert isinstance(mi.levels[0], Float64Index)
 
         assert 14 not in mi.levels[0]
-        assert not mi.levels[0]._should_fallback_to_positional()
-        assert not mi._should_fallback_to_positional()
+        assert not mi.levels[0]._should_fallback_to_positional
+        assert not mi._should_fallback_to_positional
 
         with pytest.raises(KeyError, match="14"):
             ser[14]