Arsenal were close to agreeing a fee in January for the Germany international but the player's agent expects the 20-year-old to remain in the Bundesliga
Arsenal boss 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.
The Gunners are expected to make a renewed effort to sign the Germany international in the summer but Draxler's agent, Roger Wittman, anticipates the player will remain with the Bundesliga club for another year at least despite continued interest from top clubs.
He told Sport Bild: "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"
Draxler has also been linked with a possible switch to Bayern Munich, although chairman Karl-Heinz Rummenigge said last month that the German champions were not plotting a move for the player.