The Turkish newspaper state that Fenerbahce sporting director Giuliano Terraneo has held early talks with Valencia.
Hurriyet go onto say that the Istanbul giant’s newly appointed manager Vitor Pereira is fan of Fegouli and is keen for the club to sign him this summer.
Tottenham were also closely linked with the Algeria international by the Daily Star earlier this year. The Premier League club sent scouts to monitor Feghouli’s performances but are yet to table an offer.
Valencia are understood to be holding out for €10 million for their attacking midfielder.
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.