The Germany international scored sixteen goals in all competitions in his debut season with the Gunners last season, but is set to fall down the pecking order at the club should they sign Real Madrid’s Karim Benzema.
He was substituted twenty-three times in the league last season, a record only better by former Sunderland midfielder Steed Malbranque, who was replaced on 26 occasions during the 2009/10 campaign.
Last season aside, Podolski has spent his entire career in Germany, enjoying spells with FC Koln and Bayern Munich before securing a move to the Premier League last summer.
Schalke, who initially registered an interest in Podolski back in 2007, face competition from fellow Bundesliga side Wolfsburg and Juventus in the race to secure the 28 year olds services.
He was a 94th minute substitute in Arsenal’s 3-1 defeat to Aston Villa last weekend, while he also came on late in the 3-0 victory over Fenerbache on Wednesday.