Fenerbahce have already signed two United players over the summer transfer window in Robin van Persie and Luis Nani.
Yellow Canaries board member Ilhan Eksioglu recently revealed that they are interested in making one more transfer.
Fenerbahce have already made 10 transfers this season including the likes of Lille defender Simon Kjaer, Brazil international Josef de Souza and Turkish international Ozan Tufan.
Galatasaray are also interested in strengthening the midfield over the summer and the club is under pressure to make a marquee signing after rivals Fenerbahce and Besiktas both stole the limelight over the transfer window.
The Lions won the league title for a record 20th time last season and booked a place in the Champions League group stages for the fourth consecutive season.