The Gunners tracked the 20-year-old for much of the summer after Arsene Wenger highlighted him as one of his top targets.
No official moves were made, as the Londoners instead opted to seal a club record £42.5m deal for Mesut Ozil.
Despite the arrival of the playmaker from Real Madrid, the Frenchman is still keen on Draxler, who is thought of as one of Germany’s top emerging talents.
But, Juve are also in the race, and could test Schalke’s willingness to keep hold of the starlet.
The Italian champions may make their move this winter, which would force Wenger into action.
The Emirates Stadium chief is said to have grown concerned by a lack of depth in his squad, with injuries forcing a number of youth players onto the bench for their opening Premier League fixtures.
He is believed to have around £40m at his disposal for the next transfer window, and having cast off the shackles by investing in Ozil, Wenger may dip into the market once more.
Should Arsenal break the bank for Julian Draxler?
What are your thoughts?
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