The Germany international is out of contract in June 2013 and has reportedly attracted interest from a host of top clubs, including Arsenal and Laziohere.
Schalke will reportedly try to tempt Lukas Podolski away from Koln in the summer with a lucrative contract offer.
The 26-year-old's current deal with his hometown club expires at the end of next season and has been heavily linked with a move abroad, with Lazio and Arsenal both said to be keen on signing the player.
However, according to Express, Schalke have now entered the race to sign Podolski, with club sponsors Gazprom willing to fund a move for the forward in order to boost their profile.
The paper claims that the Gelsenkirchen outfit plan to allow Jefferson Farfan to leave and effectively give his €6 million-per-season contract to Podolski, who is only on half of that wage at Koln.
Podolski has strong emotional ties with Koln and managing director Claus Horstmann insists that the club are confident of retaining the services of the Germany international.
However, the player has admitted that he has become increasingly frustrated by the club's lack of progress in recent seasons and insists that he will not make a decision on his future until after Euro 2012.