The Nigerian Captain has spent the last two seasons on loan at the Istanbul club and helped them to win a league and cup double last season.
Yobo would find himself well down the pecking order if he were to return to Goodison Park, with Phil Jagielka, John Heitinga, Sylvan Distin and Shane Duffy competing for the two centre back slots.
Talks had previously stalled on a deal to take the 31-year old to Turkey full time, with Everton’s asking price thought to be out of Fenerbahce’s price range.
It would now appear however, that the two clubs are closing in on a deal, believed to be in the region of £1.5m.
The possibility of a transfer is boosted by the fact that Yobo has reiterated his desire to remain a Fenerbahce player.
He said: “I joined them because I was eager to win silverware. I hope my permanent move is concluded soon.