Having been given just four league starts last season and finding himself on Bayern's bench behind first-choice strikers Miroslav Klose and Luca Toni, Podolski again finds himself mainly on the reserves bench this term.
The arrival of new coach Jurgen Klinsmann, plus two goals for Germany a week ago and a series of impressive performances at Euro 2008 in the summer, have done nothing to boost Podolski's position at Bayern.
After expressing his discontent in the German press recently, the 23-year-old was then told to "stop whining" about the situation by Bayern manager Uli Hoeness.
Former sweeper Sammer, 41, the German Football Federation's director of sport, says he would walk away if he was Podolski.
"In his place, I would leave Bayern," Sammer told German television channel Premiere.
Having been given just one league start so far this season, Podolski replaced Germany team-mate Miroslav Klose on 57 minutes at Cologne on Saturday and scored an injury-time goal in the 3-0 win.
He celebrated by burying his face in the turf at his former club - which he describes as his "first love" - and did not even allow himself a smile having made no secret of his desire to return to Cologne.
"It was just like when I scored two goals for Germany against Poland at Euro 2008, the celebration was as a mark of respect," said the Polish-born Podolski. "As an opposition player to be welcomed here in the way I was by the Cologne fans - that is probably unique in the world."
Spanish giants Real Madrid, plus Premier League sides Manchester City and Tottenham Hotspur have all expressed an interest in signing Podolski from Bayern when the transfer window opens in January.
"The goal was good for me: if I well play during the minutes where I am involved, then the coach has no reason to leave me out," said Podolski who has scored 30 goals for his country.