Bayern president Franz Beckenbauer says Podolski, 23, can go because he does not suit the team's style of play.
Podolski has admitted that he wants to leave Munich with his former club Cologne, City and Roma all wanting his signature.
Beckenbauer said: ''You can't keep a professional if he is unhappy, on the bench and not playing.
"Podi is a top-class striker when he has space to run clear.
"But teams we face are usually very defensive."