Podolski, who joined Bayern in 2006, has this year largely been left on the bench behind regular starters Luca Toni and Miroslav Klose.
Podolski, who had a superb 2006 World Cup under Klinsmann and has continued to score goals for the national side, has said he wants to leave, with former club Cologne the most likely destination.
The addition of striker Landon Donovan, on loan from the Los Angeles Galaxy and the signing of Croatian international Ivica Olic to join Bayern from next season has further hampered Podolski's hopes of a successful future at the Munich club.
"It hurts to see a special talent who just stops and does not progress because he cannot deal with the situation of having two players in front of him," Klinsmann told Bayern's website.
"I would have hoped he had some anger, which he would express in his game and he would say to himself: 'I will show them what I have got'", Klinsmann said.
"Bayern is a club where it is either or. Either a player faces the challenge and says 'I will fight my way into the team'... or it is better to change your environment."
Bayern are in talks with Cologne and hope to agree a deal by the end of the month, Bayern manager Uli Hoeness said last week.
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