diff --git a/src/huggingface_hub/__init__.py b/src/huggingface_hub/__init__.py
index e2ae440517..cf18c58589 100644
--- a/src/huggingface_hub/__init__.py
+++ b/src/huggingface_hub/__init__.py
@@ -89,16 +89,18 @@ def __getattr__(name):
         if name in submodules:
             return importlib.import_module(f"{package_name}.{name}")
         elif name in attr_to_modules:
-            submod = importlib.import_module(f"{package_name}.{attr_to_modules[name]}")
+            submod_path = f"{package_name}.{attr_to_modules[name]}"
+            submod = importlib.import_module(submod_path)
+            attr = getattr(submod, name)
+
+            # If the attribute lives in a file (module) with the same
+            # name as the attribute, ensure that the attribute and *not*
+            # the module is accessible on the package.
             if name == attr_to_modules[name]:
-                warnings.warn(
-                    _LazyImportWarning(
-                        "Module attribute and module have same "
-                        f"name: `{name}`; will likely cause conflicts "
-                        "when accessing attribute."
-                    )
-                )
-            return getattr(submod, name)
+                pkg = sys.modules[package_name]
+                pkg.__dict__[name] = attr
+
+            return attr
         else:
             raise AttributeError(f"No {package_name} attribute {name}")
 
diff --git a/src/huggingface_hub/snapshot_download.py b/src/huggingface_hub/snapshot_download.py
new file mode 100644
index 0000000000..888fcc1d8c
--- /dev/null
+++ b/src/huggingface_hub/snapshot_download.py
@@ -0,0 +1,14 @@
+# TODO: remove in 0.11
+
+import warnings
+
+
+warnings.warn(
+    "snapshot_download.py has been made private and will no longer be available from"
+    " version 0.11. Please use `from huggingface_hub import snapshot_download` to"
+    " import the only public function in this module. Other members of the file may be"
+    " changed without a deprecation notice.",
+    FutureWarning,
+)
+
+from ._snapshot_download import *  # noqa
diff --git a/tests/test_snapshot_download.py b/tests/test_snapshot_download.py
index b41b438a3c..d8220b3983 100644
--- a/tests/test_snapshot_download.py
+++ b/tests/test_snapshot_download.py
@@ -4,6 +4,8 @@
 import time
 import unittest
 
+import pytest
+
 import requests
 from huggingface_hub import HfApi, Repository, snapshot_download
 from huggingface_hub.hf_api import HfFolder
@@ -357,3 +359,10 @@ def test_download_model_with_ignore_regex(self):
 
     def test_download_model_with_ignore_regex_list(self):
         self.check_download_model_with_regex(["*.git*", "*.pt"], allow=False)
+
+
+def test_snapshot_download_import():
+    with pytest.warns(FutureWarning, match="has been made private"):
+        from huggingface_hub.snapshot_download import snapshot_download as x  # noqa
+
+    assert x is snapshot_download