The Lions are reported to have agreed terms with Arsenal and are on the verge of completing the transfer.
The Istanbul giants are reported to have put forward a three-year deal worth €3 million per-season and a €2 million transfer fee.
Podolski recently revealed that he wants first-team football if he is to stay at the North London based club next season.
“I can’t make any claims. I am under contract at Arsenal,” Podolski told Kicker.
“I have not talked to Arsenal yet, but if I return I want to play. I won’t sit on the bench or in the stands.”
Podolski has been closely linked with a move to the Lions and has stated that he would consider a move to Turkey.
The World Cup winner told NTV Sport: “If an offer comes from Turkey, I will sit down and talk about it with my family and girlfriend.
“If I find the right club, the right coach, the right environment, I will evaluate it.
“If these conditions are met, I think everything is possible.
“The next transfer could be my last, so I have to take a well-thought step.”
Galatasaray won the league title last season and booked a place in the Champions League group stages.