The Daily Turkish newspaper claim that both Istanbul club’s were put off by United’s asking price.
Fellaini provided one assist and scored seven goals in 31 appearances for Manchester United last season. The Belgium international was used as a make-shift striker at times by the Red Devil’s boss Louis van Gaal.
The 27-year-old has fallen down the pecking order at Old Trafford following the signings of Bastian Schweinsteiger, Morgan Schneiderlin and Memphis Depay.
Fenerbahce have already signed eight players this season including Lille defender Simon Kjaer, 2014-15 Süper Lig top scorer Fernandao, Turkish international Şener Özbayraklı and Brazil international Josef De Souza.
The Yellow Canaries take on Eskişehirspor in the opening game of the 2015-16 Turkish Super Lig season.