The 30-year-old Dutchman returned after a lengthy spell on the sidelines to score in a 3-0 win at Hamburg last weekend.
His current contract with the Gelsenkirchen club expires in 2015, but that deal is reported to include a get-out clause for this coming summer.
General manager Horst Heldt would now like to renegotiate the terms to ensure Huntelaar remains with the club.
"He fought through his rehabilitation period like an animal in order to get back quickly and we have a lot planned with him," Heldt told Sport Bild magazine.
"We're going to start talks with him and his agent soon.
"We want to work with him for a long time, but we'll have to see how things go with his condition throughout the second half of the season."
Huntelaar has no doubts about his fitness after making such an impressive return following an absence of five and a half months.
"I'd like to carry on playing for another 10 years," he told the Bild newspaper.
"I still feel young and fit and I don't look that old, do I? I want to play until I'm 40."
Huntelaar is not certain those 10 years will be spent in the Bundesliga, however.
"Of course I think about playing in England now and again, but right now my focus is on Schalke and the second half of the season," he said.
"I still have a year and a half on my contract and I think a decision over my future will be made half a year before that expires."