diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 4b074924baaf2..714a332be2196 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -6863,16 +6863,16 @@ def replace(
 
     @Appender(_shared_docs["interpolate"] % _shared_doc_kwargs)
     def interpolate(
-        self,
-        method="linear",
-        axis=0,
-        limit=None,
-        inplace=False,
-        limit_direction="forward",
-        limit_area=None,
-        downcast=None,
+        self: FrameOrSeries,
+        method: str = "linear",
+        axis: Axis = 0,
+        limit: Optional[int] = None,
+        inplace: bool_t = False,
+        limit_direction: str = "forward",
+        limit_area: Optional[str] = None,
+        downcast: Optional[str] = None,
         **kwargs,
-    ):
+    ) -> Optional[FrameOrSeries]:
         """
         Interpolate values according to different methods.
         """
diff --git a/pandas/core/internals/blocks.py b/pandas/core/internals/blocks.py
index e70c8f9d5f09a..a4a8d672895ce 100644
--- a/pandas/core/internals/blocks.py
+++ b/pandas/core/internals/blocks.py
@@ -1,7 +1,7 @@
 from datetime import datetime, timedelta
 import inspect
 import re
-from typing import Any, List
+from typing import TYPE_CHECKING, Any, List, Optional
 import warnings
 
 import numpy as np
@@ -83,6 +83,9 @@
 import pandas.core.missing as missing
 from pandas.core.nanops import nanpercentile
 
+if TYPE_CHECKING:
+    from pandas import Index
+
 
 class Block(PandasObject):
     """
@@ -1066,16 +1069,16 @@ def coerce_to_target_dtype(self, other):
 
     def interpolate(
         self,
-        method="pad",
-        axis=0,
-        index=None,
-        inplace=False,
-        limit=None,
-        limit_direction="forward",
-        limit_area=None,
-        fill_value=None,
-        coerce=False,
-        downcast=None,
+        method: str = "pad",
+        axis: int = 0,
+        index: Optional["Index"] = None,
+        inplace: bool = False,
+        limit: Optional[int] = None,
+        limit_direction: str = "forward",
+        limit_area: Optional[str] = None,
+        fill_value: Optional[Any] = None,
+        coerce: bool = False,
+        downcast: Optional[str] = None,
         **kwargs,
     ):
 
@@ -1115,6 +1118,9 @@ def check_int_bool(self, inplace):
         r = check_int_bool(self, inplace)
         if r is not None:
             return r
+
+        assert index is not None  # for mypy
+
         return self._interpolate(
             method=m,
             index=index,
@@ -1130,13 +1136,13 @@ def check_int_bool(self, inplace):
 
     def _interpolate_with_fill(
         self,
-        method="pad",
-        axis=0,
-        inplace=False,
-        limit=None,
-        fill_value=None,
-        coerce=False,
-        downcast=None,
+        method: str = "pad",
+        axis: int = 0,
+        inplace: bool = False,
+        limit: Optional[int] = None,
+        fill_value: Optional[Any] = None,
+        coerce: bool = False,
+        downcast: Optional[str] = None,
     ) -> List["Block"]:
         """ fillna but using the interpolate machinery """
         inplace = validate_bool_kwarg(inplace, "inplace")
@@ -1169,15 +1175,15 @@ def _interpolate_with_fill(
 
     def _interpolate(
         self,
-        method=None,
-        index=None,
-        fill_value=None,
-        axis=0,
-        limit=None,
-        limit_direction="forward",
-        limit_area=None,
-        inplace=False,
-        downcast=None,
+        method: str,
+        index: "Index",
+        fill_value: Optional[Any] = None,
+        axis: int = 0,
+        limit: Optional[int] = None,
+        limit_direction: str = "forward",
+        limit_area: Optional[str] = None,
+        inplace: bool = False,
+        downcast: Optional[str] = None,
         **kwargs,
     ) -> List["Block"]:
         """ interpolate using scipy wrappers """
@@ -1200,14 +1206,14 @@ def _interpolate(
                 )
         # process 1-d slices in the axis direction
 
-        def func(x):
+        def func(yvalues: np.ndarray) -> np.ndarray:
 
             # process a 1-d slice, returning it
             # should the axis argument be handled below in apply_along_axis?
             # i.e. not an arg to missing.interpolate_1d
             return missing.interpolate_1d(
-                index,
-                x,
+                xvalues=index,
+                yvalues=yvalues,
                 method=method,
                 limit=limit,
                 limit_direction=limit_direction,
diff --git a/pandas/core/missing.py b/pandas/core/missing.py
index 79bbef5fa5505..d8671616f944e 100644
--- a/pandas/core/missing.py
+++ b/pandas/core/missing.py
@@ -2,6 +2,8 @@
 Routines for filling missing data.
 """
 
+from typing import Any, List, Optional, Set, Union
+
 import numpy as np
 
 from pandas._libs import algos, lib
@@ -92,7 +94,7 @@ def clean_fill_method(method, allow_nearest=False):
     return method
 
 
-def clean_interp_method(method, **kwargs):
+def clean_interp_method(method: str, **kwargs) -> str:
     order = kwargs.get("order")
     valid = [
         "linear",
@@ -160,15 +162,15 @@ def find_valid_index(values, how: str):
 
 
 def interpolate_1d(
-    xvalues,
-    yvalues,
-    method="linear",
-    limit=None,
-    limit_direction="forward",
-    limit_area=None,
-    fill_value=None,
-    bounds_error=False,
-    order=None,
+    xvalues: np.ndarray,
+    yvalues: np.ndarray,
+    method: Optional[str] = "linear",
+    limit: Optional[int] = None,
+    limit_direction: str = "forward",
+    limit_area: Optional[str] = None,
+    fill_value: Optional[Any] = None,
+    bounds_error: bool = False,
+    order: Optional[int] = None,
     **kwargs,
 ):
     """
@@ -238,6 +240,7 @@ def interpolate_1d(
     # are more than'limit' away from the prior non-NaN.
 
     # set preserve_nans based on direction using _interp_limit
+    preserve_nans: Union[List, Set]
     if limit_direction == "forward":
         preserve_nans = start_nans | set(_interp_limit(invalid, limit, 0))
     elif limit_direction == "backward":