The Istanbul Giants are hoping the lure the French international with the prospect of Champions League football alongside a three-year contract.
Gignac visited Istanbul last Monday to check out Galatasaray’s stadium and facilities.
The French international was closely linked with a move to Dynamo Moscow but the deal fell through after the Russian giants failed to book a Champions League place next season.
Galatasaray won the Süper Lig for the 20th time and the Turkish Cup for the 16th time – the Lions sixth double. The Istanbul giants have secured a Champions League group stage spot.
Gignac was in prolific form for Marseille last season scoring 21 goals in 37 Ligue 1 appearances however, he has not renewed his contract with the French giants and is available on a free transfer.