diff --git a/dvc/config.py b/dvc/config.py
index cee34420e..f103c03b0 100644
--- a/dvc/config.py
+++ b/dvc/config.py
@@ -90,6 +90,7 @@ class Config(dict):
     def __init__(
         self,
         dvc_dir: Optional["StrPath"] = None,
+        local_dvc_dir: Optional["StrPath"] = None,
         validate: bool = True,
         fs: Optional["FileSystem"] = None,
         config: Optional["DictStrAny"] = None,
@@ -105,6 +106,10 @@ class Config(dict):
         if dvc_dir:
             self.dvc_dir = self.fs.path.abspath(dvc_dir)
 
+        self.local_dvc_dir = local_dvc_dir
+        if not fs and not local_dvc_dir:
+            self.local_dvc_dir = dvc_dir
+
         self.load(
             validate=validate, config=config, remote=remote, remote_config=remote_config
         )
@@ -140,7 +145,9 @@ class Config(dict):
 
         if self.dvc_dir is not None:
             files["repo"] = self.fs.path.join(self.dvc_dir, self.CONFIG)
-            files["local"] = self.fs.path.join(self.dvc_dir, self.CONFIG_LOCAL)
+
+        if self.local_dvc_dir is not None:
+            files["local"] = self.wfs.path.join(self.local_dvc_dir, self.CONFIG_LOCAL)
 
         return files
 
diff --git a/dvc/repo/__init__.py b/dvc/repo/__init__.py
index dea0f4558..9aee52117 100644
--- a/dvc/repo/__init__.py
+++ b/dvc/repo/__init__.py
@@ -244,6 +244,7 @@ class Repo:
 
         return Config(
             self.dvc_dir,
+            local_dvc_dir=self.local_dvc_dir,
             fs=self.fs,
             config=self._config,
             remote=self._remote,