The Turkish daily newspaper reports that the Lions are in advanced negotiations and that Podolski is expected to sign for the Istanbul giants.
“I grew up in a Turkish area and know a bit of Turkish. Champions League football is a must and Galatasaray have made a lucrative offer,” Podolski was reported as saying by Sabah.
Galatasaray sporting director Cüneyt Tanman confirmed yesterday that the Lions are targeting the World Cup winner.
“We are interested in Podolski,” Tanman told TRT.
Podolski recently underlined that he would consider a move to Turkey should an offer be made and Galatasaray have had a long term interest in the striker.
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.”
Podolski is expected to leave Arsenal this summer after falling out of of favour with Arsenal boss Arsene Wenger.
The Germany international joined Inter on loan in January but failed to impress scoring just on Serie A goal.
Galatasaray won the league title last season and booked a place in the Champions League group stages for the fourth consecutive season.