The Dutch striker could become the club's highest-ever paid player by signing a new deal beyond 2013 after impressing this season.
The former Real Madrid and AC Milan striker has scored 38 goals in 37 appearances for the Royal Blues in all competitions this campaign, attracting the interest of several top European clubs as a result.
And general manager Horst Heldt wants to warn them away from the 28-year-old by making him an offer he cannot refuse.
"If we want quality, then we have got to push ourselves to the pain barrier," he told the Bild newspaper.
"We will not tie Huntelaar to the negotiation table and torture him, but he does know that we really value him here, and he feels happy here too."
Schalke are keen to extend Huntelaar's contract before the end of the season since he reportedly has a clause in his current deal which would allow him to leave the club if an offer in excess of 20 million euros is received.