The Bundesliga side said on its website that it held talks with Podolski and his adviser on Tuesday to discuss the 28-year-old’s contract, which expires in June 2013.
Cologne said talks took place “in a positive and constructive atmosphere” but that neither side would give further details.
Podolski is enjoying his best season with 14 goals so far for his hometown club.
British newspaper The Guardian reported Monday that Podolski ruled out a January transfer to Arsenal to safeguard his place for Germany at the 2012 European Championships.
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