The Turkish transfer window is on the home stretch and closes for clubs in the country on Friday.
Nottingham Forest striker Emmanuel Dennis is the latest player from the Premier League to have been linked with a move to Turkey and now Gomes has joined him.
The Everton midfielder is now drawing interest from Fenerbahce, according to Turkish outlet Sports Digitale.
Gomes spent last season in France with Lille, for whom he featured in 26 league games making five goal contributions.
He has less than a year left on his current contract at Goodison Park and is not currently an essential part of manager Sean Dyche’s plans.
Everton boss Dyche has other players ahead of Gomes and the Toffees could see an opportunity to let him go.
Whether Gomes would be open to the prospect of a move to Turkey with Fenerbahce remains to be seen.