The 28-year-old forward has been linked with a return to Germany after enduring a frustrating time in the Premier League since joining Arsenal from Koln last summerSchalke head coach Jens Keller has refused to discuss rumours linking Arsenal attacker Lukas Podolski to the club.
Goal revealed on Friday that the Bundesliga outfit had proposed a move for the Germany international as part of a swap deal involving Gunners target Atsuto Uchida - though the north Londoners are adamant the 28-year-old is not for sale.
But Keller, whose Schalke side are also reportedly close to signing Polish midfielder Waldemar Sobota from Slask Wroclaw, would not be drawn on either potential signing ahead of his side's clash with Hannover.
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"There are a few players on our list and we will see what we can do about it and what possibilities there are."
Schalke's season has begun badly, picking up just a solitary victory against Noettingen in the DFB Pokal and yet to win in the league, and Keller says the players are disappointed with their displays so far.
"Well the guys are not crazy, they are aware of the fact that they aren't completely performing to their best and they aren't happy about that," Keller said.
"So no one said, 'well I was great and others weren't'. I mean, of course, it's not like that. They're all critical of themselves and that's good.
"And I have always said the team has the right character, we just have to make the transition to the pitch. And that's what counts in football. No one has ever won by talking."