The Gelsenkirchen outfit remains hopeful that the attacking midfielder will stay at his current club for an additional season.
The Premier League giants are keen to lure the 20-year-old away from his current club either this winter or at the end of the season, but Schalke remains hopeful that Draxler will commit his future to the Gelsenkirchen side.
"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."
Draxler has a contract with Schalke until June 2018, but his current deal contains a 45.5-million-euro release clause.