The Lions boss stated that an offer was made for the Germany international in January but that the club is no longer pursuing Podolski.
“Podolski is not on our radar right now, he was in the winter but not right now,” Hamzaoğlu told TRT.
Werder Bremen have also pulled out of the race to sign Podolski according to club general manager Thomas Eichin.
“Lukas Podolski is a great footballer, I like him,” Sky Sports quotes Eichin as saying.
“But we do not need to discuss such rumours. It is totally unrealistic for us to make a move for him.”
The Germany joined Inter on loan in January but struggled to settle in and only scored on goals in the Seria A.
Podolski is expected to leave Arsenal in the summer and Galatasaray were reported to be holding talks with the experienced striker.
The Lions are reported to have held talks with the World Cup winner who only has one year remaining on his contract.
Galatasaray won the league for the 20th time and the Turkish Cup for the 16th time – their sixth double.