Dortmund have already announced the departure of Mario Gotze to Bayern Munich this summer and top goalscorer Robert Lewandowski is set to follow his team mate to join Pep Guardiola at the Allianz Arena.
The combined fees could be in the region of £75million, allowing Dortmund to rebuild their squad to challenge in the Bundesliga once again and Draxler has been pinpointed as their number one target.
Arsenal boss Arsene Wenger has scouted the 19-year-old German international on numerous occasions but the Gunners may not be able to compete financially with Dortmund.
Schalke want £15million for their academy product and the attacking midfielder will have an easy decision to make if Arsenal fail to qualify for next seasons Champions League.
Plenty of European rivals may join the race for Draxler so Wenger is hoping to do his business early this summer.
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