According to the Daily Express, the Bundesliga side are ready to reward Huntelaar with a new contract to ward off interest from the likes of Arsenal, Liverpool and Tottenham Hotspur.
The 31-year-old Dutch international will be a free agent next summer, and Schalke are desperate to avoid a situation where he could leave the club for nothing.
The former-Real Madrid striker is currently undecided over his destination for next season, and could be tempted by a sojourn in the Premier League.
Arsenal were linked with a deadline day move for the £12.5m rated Huntelaar this summer, but ultimately completed a £16m deal for Danny Welbeck. The forward capped a good England performance with two goals for his country last night, and is hoping to play through the middle at the Emirates Stadium.
He will get his chance with Olivier Giroud out until December at the earliest, but Arsene Wenger may still be tempted to go back into the market for an out-and-out centre-forward in January if Welbeck doesn't work out and is forced into a wide role.
Arsenal transfer round-up
Huntelaar's goal record
Huntelaar has been prolific in Germany, scoring 60 goals in 101 Bundesliga appearances. His record for his country is just as good, as the Dutchman has bagged 35 in 65 caps since his debut in 2006.
As for Liverpool, they snapped up Mario Balotelli for £16m last month. Like Tottenham, they are just monitoring Huntelaar in case injuries strike between now and the January transfer window.