The 21-year-old midfielder has been tipped to leave Schalke this summer, with Arsenal boss Arsene Wenger keen to sign some top quality additions to his squad.
The Bianconeri are thought to be in 'no rush' to land Draxler, although they have had a £15.6million bid rejected.
Italian publication Tuttosport claimed today Manchester City's Samir Nasri is on Juve's radar as they seek a replacement for Arturo Vidal.
And the same publication claims that while Schalke won't listen to more offers for Draxler, Juve remain undeterred.
They suggest a new offer is forthcoming, although the size of the bid remains unknown.
Juventus have been active so far this window and have made three signings - Paulo Dybala, Mario Mandzukic and Sami Khedira.
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