The 20-year-old has been heavily linked with a move to Premier League leaders Arsenal, who are thought to be in the market for attack-minded reinforcements after Theo Walcott was ruled out for the rest of the season with a cruciate ligament injury.
Draxler's impressive performances have earned him international recognition, and he has 10 caps to his name for Germany so far.
However, Tonnies feels that the youngster should prolong his stay with the Gelsenkirchen outfit, and says that Schalke have no need to sell one of their prized assets.
"I am of the opinion that Julian should play for Schalke next season. That's my personal advice to him," Tonnies told Sport Bild.
"He should not let the interest from abroad play with his head. It's best for his development when he can play without much pressure and with a clear mind.
"Looking back, at the start of the season he was under a lot of pressure then and the exact same thing will happen again if he moves.
"There are a number of big clubs after him, but we have no intention of selling him this winter. Even if we do not qualify for next year's Champions League, that doesn't mean we will have to sell Julian."
