The Lion’s – who have a long standing interest in the Senegal international – are preparing to table a bid for the striker according to Fotomac.
Everton signed Niasse on a £13.5 million deal from Lokomotiv Moscow in January making him the third most expensive signing in the Toffees history.
However, the pacy striker has struggled since joining Everton and has failed to find the back of the net in five Premier League appearances.
Niasse first made a name for himself in Turkey establishing himself as one of the most sought after strikers in the Super League before moving to Russia for €5 million.
Galatasaray are after a new striker after offloading their top goalscorer Burak Yilmaz in January without signing a replacement.
Niasse previously played for Akhisar Belediyespor in the Turkish Super lig where he scored 15 goals in 40 appearances.