The Turkish daily newspaper has reported that the Lions are in talks with the World Cup winner and that Arsenal are keen to sell.
The Istanbul giants have been linked with Podolski for the past four seasons and made an offer for the 30-yera-old striker in January but he joined Inter on loan.
The Germany international had an unsuccessful spell with the Serie A giants scoring just one league goal.
Inter decided not to keep him on and Podolski returned to Arsenal where he will decide his future.
Podolski is unlikely to stay at Arsenal after falling out of favour with Gunners boss Arsene Wenger but still has a year left on his contract.
The experienced striker won the World Cup with Germany last season and wants regular first team football to keep his place in the national team side.