According to The Telegraph, Chelsea are considering the option of loaning out Chilwell, even though they initially hoped to sell him.
Fener are keen and can close a deal for the fullback with their transfer window open until September 13.
During the summer, Fenerbahce lost left-back Ferdi Kadioglu, 24, to Brighton.
Chilwell has a contract with Chelsea that runs until the summer of 2027.