Altay Bayindir is already unsettled at Manchester United.
The Turkey goalkeeper only joined United in September from Fenerbahce.
But Fotomac says Galatasaray are eyeing Bayindir for January and the keeper is open to the move.
Bayindir is yet to play for United - including at reserve-team level.
The 25 year-old keeper featured for Turkey in their friendly win against Germany this week.