Reports have claimed that the Bundesliga outfit are interested in bringing the Germany international back to his home country after falling behind Olivier Giroud at ArsenalSchalke general manager Horst Heldt has declined to comment on rumours linking them with a move for Arsenal forward Lukas Podolski.
The Germany international, who joined the Gunners from Koln in July 2012, was a second-half substitute as Arsene Wenger's side ran out comfortable 3-0 winners over Fenerbahce in the first leg of their Champions League play-off round clash on Wednesday.
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The 28-year-old will have to compete with the likes of Olivier Giroud and Theo Walcott for a place in the Arsenal starting XI, and Galatasaray, Tottenham and Schalke have all been linked with his services.
Schalke are thought to be particularly keen to bolster their forward line after star striker Klaas-Jan Huntelaar was sidelined with a knee injury sustained in their 4-0 defeat to Wolfsburg on Saturday.
Jens Keller's men drew 1-1 with PAOK in their Champions League play-off at the Veltins Arena on Wednesday, with Heldt refusing to be drawn on speculation surrounding Podolski.
"There's nothing I can say now," Heldt told Bild.
Schalke travel to Hannover on Saturday, with Adam Szalai - recruited from Bundesliga rivals Mainz in June - expected to lead the attack in Huntelaar's absence.