Draxler was subject of a considerable bid from an unnamed club this winter, widely reported to be Arsenal, and while he can leave for a set fee of 45.5million euros (£37.7m) in the summer, Tonnies hopes he will stay.
"It would do Draxler good to spend another year or two with us," said Tonnies at the SpoBiS exhibition in Dusseldorf.
"But we know we're not going to be able to keep a super-talented player like Julian at Schalke forever.
"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."
Draxler is still contracted to Schalke until 2018 but interest is growing in the 20-year-old, who became the youngest Bundesliga player to make 100 appearances while still only 19 last March.
A player for the future but i think wenger was right not to buy him in january he would not have won us the league singlehandedly (which is what some gooners seem to believe..)- paulino971