Arsenal attempted to bring the attacking midfielder to the Emirates Stadium in January, and are believed to still be interested in his services as they prepare to enter the transfer market once again this summer.
However, Torries believes that the 20-year-old is likely to spend at least one more season at the club.
"If nothing extraordinary happens, Julian will stay with us," the Schalke chairman told Bild.
"I am convinced that he will play even longer than this one next season at Schalke. Then we will see"
Reports earlier this week suggested that Draxler and Real Madrid forward Alvaro Morata were Arsenal's top targets ahead of next season.