Schalke's director of sport Horst Heldt said: "We want to extend his contract and I believe that it would make sense for both parties.
"But we need him to be 100% convinced. I cannot force any player to sign a new contract."
Heldt is also aware that Huntelaar is hardly lacking offers to tempt him away from the club.
"Klaas Jan is an absolutely top-level footballer and of course he will have other options," he added.