British newspaper the 'Guardian' is reporting that Florentino Perez is looking to splash the cash on the Austria international.
Madrid are looking for a left-back to compete with Marcelo and have targeted the Bayern Munich man as a potential signing.
Zidane's side are yet to make a marquee summer signing, but this may be about to change if they opt to bid for the 24-year-old.
The Champions League winners were considering a move for Newcastle's Moussa Sissoko as their major signing this transfer window, but Zidane rejected the idea of bringing the Frenchman to the Bernabeu.