The Gelsenkirchen side rejected a bid from Juventus for the 21-year-old earlier this summer but a fresh offer could see the playmaker move.
Schalke chief Horst Heldt said he has received no fresh offers for Julian Draxler but admitted the Germany international could still leave the club.
The 21-year-old had appeared set to join Juventus earlier this summer but S04 rejected a bid worth up to $22 million for his services as the club felt it was inadequate.
General manager Heldt insisted Schalke has no plans to sell its star asset but acknowledged that could all change prior to the end of the transfer window.