Robben has been closely linked with a move for the Netherlands international and the Milliyet claimed that the Yellow Canaries had made a bid for the experienced winger.
There was further speculation that a transfer could be on the cards following Robben not joining the rest of the Bayern squad on the China tour.
The Yellow Canaries did however, put forward a €6 million offer for the 31-year-old winger last season according to the Akşam newspaper.
Fenerbahçe are expected to make another signing should they progress past Shakhtar Donetsk in the Champions League preliminary play-off tie.
Fenerbahçe also signed fellow United player Nani on a three-year deal. Lille defender Simon Kjaer, last seasons top scorer Fernandao and Brazil international Josef De Souza also joined the Yellow Canaries over the summer.