The report claims that Fenerbahçe boss Vitor Pereira wants an additional central midfielder and has added the Blues star to his shortlist.
The Telegraph however, report that Ramires is unlikely to part ways with the Premier League champions over the summer.
The Blues are in talks with the Brazil international midfielder over a contract extension deal.
The 28-year-old is expected to sign a new agreement with the club after successful talks between the player and Chelsea.
Ramires already had two-years left on his current deal but Chelsea are keen on securing his long term future at the club.
The Yellow Canaries have also completed the transfer of Lille defender Simon Kjaer, Turkish international Sener Ozbayrakli and last seasons goal king Fernandao.