The forward has refused to commit his long-term future to his hometown club, while coach Stale Solbakken has likened him to Barcelona's Lionel Messi
The striker has a reputation for being loyal to his hometown club and is well regarded by the management at his current team, but could leave for sporting or financial reasons.
"I can jump to no conclusions about my future," he said according to Express.
"I have always stressed that my future is open and said that I will have to wait and see about the state of the club's sporting situation.
"I am pleased that things are going so well for me, but I also know that football is a daily business."
Podolski has been a key figure for Koln this season, scoring or assisting 11 of his team's 18 goals. For his fine performances, he has been repeatedly praised by coach Stale Solbakken.
"Lukas is perhaps the Bundesliga's best player," the trainer told Bild. "Barcelona are not Barcelona without Messi. Koln are not Koln without Poldi."
Podolski left the club for a bigger stage earlier in his career - he spent three years at Bayern Munich - and if Koln are unable to qualify for European competition or offer him a sufficient contract extension past 2013, he may be tempted to move elsewhere.
Koln have earned 16 points from their first 11 games, and despite their position of 11th in the Bundesliga table, are only two points away from a Europa League spot.