The playmaker has once more underlined his commitment to the Champions League chasers, while general manager Horst Heldt has priced him at a lofty €100 million (£84m)
The 19-year-old has been linked with a move to rivals Borussia Dortmund since Mario Gotze's €37 million (£31m) switch to Bayern Munich was confirmed last month, although the player himself suggested that only "brainwashing" would make him consider joining BVB.
And Draxler, who scored the winning goal in Schalke's vital 1-0 win over Borussia Monchengladbach in their bid to secure Champions League football next season, has reiterated his belief that he has not played his final match at the Veltins Arena, despite being suspended for the final home game of the campaign following his yellow card on Friday.
"I very much assume that I will be playing here next season," he was quoted as saying by Bild.
"That was a really big win. We are all very happy. I'm just sorry that I won't be playing at the last home game. That was not the smartest action from me."
General manager Horst Heldt added his intention to keep Draxler at the club for the foreseeable future, barring a mega-money bid from one of Europe's elite.
"We want to keep Julian for a long time," Heldt said. "But if Barcelona or Real Madrid offer €100m..."