كتب : Omar AbdelAziz
During the past few weeks, Cologne were determinant to land their former star, but Bayern's asking price hindered the deal.
"They have made a new bid and it looks fine," Bayern chairman Karl-Heinz Rummenigge said on Thursday.
"There is no big difference any more, though I'm confident this could really happen."
Podolski came through Cologne's youth ranks before joining the Bavarian giants in 2006.
His career at Bayern took a back seat to the team's preferred partnership of Miroslav Klose and Luca Toni.
The 23-year-old, who excelled with Germany in EURO 2008, voiced his desire to leave Bayern more than once as he seeks to play regular first-team football.