Arsene Wenger targeted the 20-year-old forward in January and was close to agreeing a fee with the German club before the transfer collapsed shortly before the window deadline.
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He told SportBild.de: "Why should a player leave the club if the club have just built a top team? I also think it's good if players stick to what they have signed.
"It would take an awful lot to happen for one of the two [Draxler or Jefferson Farfan] to leave. And even then I'm not sure it would be possible.
"The players understand that there is currently a lot of peace at the club and a lot of optimism about their future there."
Those sentiments were echoed by Schalke chairman Clemens Torries, who said: "If nothing extraordinary happens, Julian will stay with us.
"I am convinced that he will play even longer than this one next season at Schalke. Then we will see"