Garnacho, an Argentine international, has been told to find a new club after having a disagreement with his previous coach, Ruben Amorim, at the end of last season.
Recently, there were rumors that Garnacho might join Chelsea or Aston Villa, but now Fenerbahce is also making its interest known.
The coach of Fenerbahce, Jose Mourinho, fully supports the possible transfer of Garnacho to Istanbul.
Fenerbahce is willing to make a strong effort to bring Garnacho to their team, despite Manchester United valuing him at £50-70m.