The Turkish newspaper Fanatik have stated that the the Blues are willing to offload the Ghana international following a turbulent season.
Fanatik go onto say that the Yellow Canaries are hoping to sign Rahman for a lower price that the Blues payed for him.
Fenerbahce are on the hunt for a new left-back after failing to agree a new deal with their current first choice Caner Erkin. The Turkish international is expected to leave in the summer meaning the Istanbul Giants are in need of a replacement.
Rahman joined Chelsea from Augsburg but the 21-year-old has failed to make an impact since his £14 million move.
The Ghana international has made a total of 12 Premier League appearances for the London based club this season.
Fenerbahce signed eight players earlier this season including Lille defender Simon Kjaer, 2014-15 Süper Lig top scorer Fernandao, Turkish international Şener Özbayraklı and Brazil international Josef De Souza.