The report comes amid a report from AMK which states that the Istanbul Giants are close to agreeing personal terms with the Algeria international.
Feghouli is understood to be open to a move away from Spain this summer, with Valencia likely to miss out on European football next season.
Feghouli’s contract with Valencia expires at the end of the season meaning he is able to discuss personal terms with clubs and leave on a free in July.
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.
Feghouli has four assists and seven goals in 36 appearances for Valencia this season. The 26-year-old has made 39 appearances for the Algerian national team.