The Toffees were eager to move on from the Portuguese central midfielder.
However, Gomes was unable to secure a move away, despite interest from several teams.
Per Sporx in Turkey, Fenerbahce were the club that had the best chance to secure his signature.
However, the Turkish giants decided against the move, as they did not feel he would sufficiently improve the team.
Gomes has struggled to find his best form since an ankle injury he sustained a few years ago.