diff --git a/pandas/core/window/expanding.py b/pandas/core/window/expanding.py
index ec4c23bfc5e49..aac10596ffc69 100644
--- a/pandas/core/window/expanding.py
+++ b/pandas/core/window/expanding.py
@@ -5,6 +5,7 @@
     TYPE_CHECKING,
     Any,
     Callable,
+    Literal,
 )
 
 from pandas.util._decorators import (
@@ -231,7 +232,7 @@ def apply(
         self,
         func: Callable[..., Any],
         raw: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
         args: tuple[Any, ...] | None = None,
         kwargs: dict[str, Any] | None = None,
@@ -275,7 +276,7 @@ def apply(
     def sum(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         return super().sum(
@@ -314,7 +315,7 @@ def sum(
     def max(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         return super().max(
@@ -353,7 +354,7 @@ def max(
     def min(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         return super().min(
@@ -392,7 +393,7 @@ def min(
     def mean(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         return super().mean(
@@ -431,7 +432,7 @@ def mean(
     def median(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         return super().median(
@@ -490,7 +491,7 @@ def std(
         self,
         ddof: int = 1,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         return super().std(
@@ -550,7 +551,7 @@ def var(
         self,
         ddof: int = 1,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         return super().var(
diff --git a/pandas/core/window/rolling.py b/pandas/core/window/rolling.py
index d26c405a34e87..ec48e9c9eb46a 100644
--- a/pandas/core/window/rolling.py
+++ b/pandas/core/window/rolling.py
@@ -13,6 +13,7 @@
     TYPE_CHECKING,
     Any,
     Callable,
+    Literal,
     cast,
 )
 
@@ -1458,7 +1459,7 @@ def apply(
         self,
         func: Callable[..., Any],
         raw: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
         args: tuple[Any, ...] | None = None,
         kwargs: dict[str, Any] | None = None,
@@ -1525,7 +1526,7 @@ def apply_func(values, begin, end, min_periods, raw=raw):
     def sum(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         if maybe_use_numba(engine):
@@ -1547,7 +1548,7 @@ def sum(
     def max(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         if maybe_use_numba(engine):
@@ -1569,7 +1570,7 @@ def max(
     def min(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         if maybe_use_numba(engine):
@@ -1591,7 +1592,7 @@ def min(
     def mean(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         if maybe_use_numba(engine):
@@ -1613,7 +1614,7 @@ def mean(
     def median(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         if maybe_use_numba(engine):
@@ -1635,7 +1636,7 @@ def std(
         self,
         ddof: int = 1,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         if maybe_use_numba(engine):
@@ -1659,7 +1660,7 @@ def var(
         self,
         ddof: int = 1,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         if maybe_use_numba(engine):
@@ -2021,7 +2022,7 @@ def apply(
         self,
         func: Callable[..., Any],
         raw: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
         args: tuple[Any, ...] | None = None,
         kwargs: dict[str, Any] | None = None,
@@ -2101,7 +2102,7 @@ def apply(
     def sum(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         return super().sum(
@@ -2141,7 +2142,7 @@ def max(
         self,
         numeric_only: bool = False,
         *args,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
         **kwargs,
     ):
@@ -2184,7 +2185,7 @@ def max(
     def min(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         return super().min(
@@ -2233,7 +2234,7 @@ def min(
     def mean(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         return super().mean(
@@ -2275,7 +2276,7 @@ def mean(
     def median(
         self,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         return super().median(
@@ -2333,7 +2334,7 @@ def std(
         self,
         ddof: int = 1,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         return super().std(
@@ -2392,7 +2393,7 @@ def var(
         self,
         ddof: int = 1,
         numeric_only: bool = False,
-        engine: str | None = None,
+        engine: Literal["cython", "numba"] | None = None,
         engine_kwargs: dict[str, bool] | None = None,
     ):
         return super().var(