The Daily Express have reported that the former German international has agreed a two-year deal with the Super Lig side and could fly out to Istanbul on Tuesday to formalise the agreement.
The Gigliati are likely to receive a transfer fee of around €8 million whereas Gomez is expected to earn up to €3.5 million per season.
Gomez struggled to make a huge impact during his time in Tuscany and managed just seven goals in 29 appearances.
The Gigliati will now turn their attention to bringing in a new striker, with Roma’s Mattia Destro and former Juventus forward Mirko Vucinic on the club’s shortlist.