diff --git a/Lib/importlib/_bootstrap.py b/Lib/importlib/_bootstrap.py
index c4ee41a..d9885c9 100644
--- Lib/importlib/_bootstrap.py
+++ Lib/importlib/_bootstrap.py
@@ -1443,7 +1443,8 @@ class SourceLoader(_LoaderBasics):
         Implementing this method allows the loader to read bytecode files.
         Raises IOError when the path cannot be handled.
         """
-        return {'mtime': self.path_mtime(path)}
+        return {'mtime': float(_os.environ.get(b'SOURCE_DATE_EPOCH',
+                                               st.st_mtime))}
 
     def _cache_bytecode(self, source_path, cache_path, data):
         """Optional method which writes data (bytes) to a file path (a str).
@@ -1580,7 +1581,10 @@ class SourceFileLoader(FileLoader, SourceLoader):
     def path_stats(self, path):
         """Return the metadata for the path."""
         st = _path_stat(path)
-        return {'mtime': st.st_mtime, 'size': st.st_size}
+        return {
+            'mtime':  float(_os.environ.get(b'SOURCE_DATE_EPOCH', st.st_mtime)),
+            'size': st.st_size
+        }
 
     def _cache_bytecode(self, source_path, bytecode_path, data):
         # Adapt between the two APIs