The 34-year-old joined Schalke in 2010, but his current contract with the club expires at the end of the season.
Raul has recently been linked with the likes of Manchester City and Blackburn Rovers.
Tonnies told Sport Bild: “Such an experienced player is very important for our young team and he proves that in every game.
“He is incredibly endearing. I have made it absolutely clear to him that he belongs with Schalke.
“We are proud for every minute that Raul plays in a Schalke shirt.
“When somebody plays good football, gets involved and identifies himself with the club, then there is nothing to say you should not continue with him.
“Financially, we can afford Raul. We have such a solid financial base that we would not have any difficulties even if we don’t qualify for Europe.”
