The Lion’s have switched their attentions back to Podolski after failing to land Andre Ayew and André-Pierre Gignac.
Podolski is expected to leave Arsenal this summer after fallout of of favour with Arsenal boss Arsene Wenger. The 30-year-old spent the second half of last season out on loan at Inter Milan.
The Germany international failed to impress Inter boss Roberto Mancini and has returned to Arsenal.
The Akşam newspaper recently stated that Galatasaray 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.”
Galatasaray won the league title last season and booked a place in the Champions League group stages.