The Istanbul club want to add to their firepower in the ongoing transfer window as they look to maintain their grip on the top of the Turkish Super Lig.
Their search has led to Selhurst Park and Galatasaray are keen on signing Mateta.
According to Turkish daily Fanatik, Galatasaray have held talks with Crystal Palace over a loan with an option to buy.
It is claimed that the talks were positive and Galatasaray feel that Mateta fits the bill in what they are looking for from a striker.
Coach Okan Buruk wants a striker who is strong physically and good in the air, and he has given his approval to a move for Mateta.
Mateta has been restricted to mainly appearances from the bench for Crystal Palace this season and has found the back of the net just once in the league, in a win over Aston Villa.
Galatasaray are prepared to terminate Haris Seferovic’s loan from Benfica to make room for Mateta in their squad.