Draxler was the subject of intense speculation during the January transfer window, with Arsenal thought to be keen on signing the 20-year-old for almost £38m.
Tonnie acknowledged that they wouldn't be able to keep the player if a big club matched his valuation, but hinted that he had no desire to join the reigning German and European champions.
"If another club comes in for him, then we cannot block them. That would be unfair. I don't think he wants to join Bayern Munich, though," Tonnies told reporters.
Schalke are currently fourth in the Bundesliga table having won both of their matches since the league season restarted.