The striker spent last season on loan at Old Trafford from Monaco but he endured a miserable time under Louis van Gaal.
The Colombian scored just four times in 29 appearances and he has fared little better at Chelsea this season.
Falcao moved on a season-long loan to the Blues in the summer but injuries have restricted him to one goal in 11 games.
Chelsea are considering cancelling the loan and that, according to Takvim, has sparked interest from Fenerbahce.
The Turkish giants are keen on a move for Falcao and are now set to contact Monaco to see whether a deal can be completed.