Since leaving Shanghai SIPG in November 2017, the Portuguese coach has taken time out of football, devoting his time to projects such as racing at the Dakar Rally.
Zidane, meanwhile, left the La Liga club last month despite guiding them to their third consecutive Champions League triumph.
According to French outlet RMC Sport, Real have earmarked Villas-Boas for the role of head coach at the Bernabeu and have already been in touch with the tactician.
The report claims that Villas-Boas's prior work experience with Gareth Bale, having managed the Welshman at Spurs, is one of the reasons for Madrid's interest in the 40-year-old.
Villas-Boas also won the Primeira Liga title and the Europa League at Porto, and guided Zenit St Petersburg to top spot in the Russian Premier League.