Horst Heldt, the club's general manager, believes the duo would have no reason to leave the Veltins Arena, but regardless he has not seen any offers come his way
The Dutchman enjoyed a fantastic season where he scored 49 goals in all competitions and led his side to third place in the Bundesliga and the Europa League quarter-finals, but has just one year left on his contract.
With the player failing to extend his deal to date, there had been speculation that nouveau riche Spanish side Malaga could move for him, but Heldt has told Huntelaar that a move to Andalusia would be a step down.
"Klaas-Jan has always stressed that he wants to be a champion," Heldt told Bild. "At the moment in Spain only Barcelona and Real Madrid can be champions.
"I don't think he wants to go there [to Malaga]. What can he do there? There's more to it than better weather."
Meanwhile, Howedes has emerged as a transfer target for Bayern Munich, as revealed by Goal.com, and is the subject of growing speculation linking him with Real Madrid, but Heldt says he is unaware of any interest.
"I've also read about Real," he continued. "But I'm not aware of anything. And we also want to build, not sell!"
Schalke will compete in the Champions League next season, having finished in the top-three of the Bundesliga, giving them an automatic ticket to the group stage.