Huntelaar, 29, has been repeatedly linked with the likes of Liverpool and Arsenal, but instead signed a new contract at the Bundesliga club.
That runs until the summer of 2015, and the former Milan hit-man said he would be willing to sign another extension.
“It’s possible that I will prolong my stay with Schalke again,” he told Bild. “At nearly 32 I could still sign another contract.
“Therefore, it is possible that I would finish my career here.”
Huntelaar has only scored six goals so far this season, compared to the 29 he hit last time out which topped the German goal charts.
That has been largely due to a relatively poor showing by his team, who have found combining the Champions League and domestic football difficult.
They currently lie sixth in the Bundesliga after Huntelaar scored in a 4-1 win over Wolfsburg.