diff --git a/discord/ext/commands/core.py b/discord/ext/commands/core.py
index 4fc6792ea..c1cc0a3ea 100644
--- a/discord/ext/commands/core.py
+++ b/discord/ext/commands/core.py
@@ -2453,6 +2453,10 @@ def cooldown(
 
         .. versionchanged:: 1.7
             Callables are now supported for custom bucket types.
+
+        .. versionchanged:: 2.0
+            When passing a callable, it now needs to accept :class:`.Context`
+            rather than :class:`~discord.Message` as its only argument.
     """
 
     def decorator(func: Union[Command, CoroFunc]) -> Union[Command, CoroFunc]:
diff --git a/docs/migrating.rst b/docs/migrating.rst
index 9e0175af9..52fe217d9 100644
--- a/docs/migrating.rst
+++ b/docs/migrating.rst
@@ -153,7 +153,6 @@ The following have been changed to :func:`runtime-checkable <typing.runtime_chec
 
 - :class:`abc.Snowflake`
 - :class:`abc.User`
-- :class:`abc.PrivateChannel`
 
 The following have been changed to subclass :class:`~typing.Protocol`:
 
@@ -163,6 +162,7 @@ The following have been changed to subclass :class:`~typing.Protocol`:
 The following have been changed to use the default metaclass instead of :class:`abc.ABCMeta`:
 
 - :class:`abc.Messageable`
+- :class:`abc.PrivateChannel`
 
 ``datetime`` Objects Are Now UTC-Aware
 ----------------------------------------
@@ -1472,6 +1472,8 @@ Miscellaneous Changes
 
     - To override a cog, the new ``override`` parameter can be used.
 
+- When passing a callable to ``type`` argument of :meth:`~ext.commands.cooldown`,
+  it now needs to accept :class:`~ext.commands.Context` rather than :class:`Message` as its only argument.
 - Metaclass of :class:`~ext.commands.Context` changed from :class:`abc.ABCMeta` to :class:`type`.
 - Changed type of :attr:`ext.commands.Command.clean_params` from :class:`collections.OrderedDict` to :class:`dict`.
   As the latter is guaranteed to preserve insertion order since Python 3.7.