A source within the club has revealed to Turkish-Football that despite having a loan bid rejected earlier this month, Galatasaray are preparing a second offer.
The Lions are keen to sign Niasse on a season-long loan but are unwilling to pay a loan-fee for the 25-year-old striker.
Niasse joined Everton from the Russian League side Lokomotiv Moscow for £13,5 million earlier this year but has failed to impress since making the move. The Senegal international was unable to find the back of the net in the Premier League last season.
Besiktas are also understood to be interested in signing Niasse. According to the Turkish outlet Hurriyet, Besiktas President Fikret Orman has traveled to England and will hold talks with Everton over Niasse. The daily turkish paper goes onto state that the Black Eagles are in contact with both Everton and Niasse.