During the summer window, Fenerbahce had been keen on giving Niasse a way out of Goodison Park with the attacker then having no part to play in the plans of Ronald Koeman.
Niasse has since gone on to score six goals this season, but the Senegalese international has made just three starts for the Toffees in all competitions.
According to Fotomac, Fenerbahce are considering whether to take advantage of his situation on Merseyside at the start of 2018.
The Turkish giants would need to sell players before they could launch a big-money offer for the 27-year-old, but it appears that they are willing to part ways with Robin van Persie.
Niasse still has two and a half years remaining on his contract with the Premier League side.