The 34-year-old has just 10 months left on his current contract with the Bundesliga side and has recently been linked with a move to the Premier League.
“I am proud with every minute that Raul plays for Schalke,” Schalke chairman Clemens Tonnies told Sport1.
“He is an amazing personality. We will wait to see how the season goes and then find the right moment to discuss whether he could maybe add another year on.”
Schalke are also keen for Peru international Jefferson Farfan to signa new contract with the club.
Tonnies added: “I am not out to hype that, but we will certainly do all we are allowed to. We want to keep Jefferson Farfan at Schalke 04.”