Draxler, a target for Arsenal, was subject of a considerable bid from an unnamed club this winter and while he can leave for a set fee of 45.5million euros (£37.8million) 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 ever Bundesliga player to make 100 appearances while still only 19 last March.
While Draxler's future remains in doubt, Klaas-Jan Huntelaar has insisted leaving Schalke "is not part of the plan" after making a winning return to action this year.
The Dutchman ended five and a half months of injury agony by inspiring the Royal Blues to back-to-back victories in 2014.
As a result, Schalke are back up to fourth in the Bundesliga and on course to achieving their primary objective for the season, and Huntelaar sees no reason to be anywhere else.
"Our priority is qualifying for the Champions League," he said in Sport Bild magazine. "We could still even finish second, but we shouldn't make things unnecessarily complicated for ourselves but rather take things from game to game.
"I still have 18 months on my contract here and I'm just delighted to be back on the field again. All I am thinking about is the second half of the season."
Huntelaar is reported to have a release clause in his contract, which expires in 2015, but he does not care for that.
"I don't know all the precise details of my contract, but that doesn't play a role anyway," he said.
"I'm fully focused on Schalke. Leaving Schalke is not part of the plan."