Los Blancos do not want to risk losing their key defender for free so they are willing to cash in this summer, according to the MEN.
Ole Gunnar Solskjaer is desperate to bring in a permanent partner for £80million man Harry Maguire.
Eric Bailly and Victor Lindelof have had varied success this season but neither are seen as the long-term solution.
Varane has been high on Ed Woodward’s wishlist for many years and the United chief is now the closest he has ever been to landing his target.
Zidane has apparently agreed for a captaincy clause to be included in the deal to tempt Varane to extend his 10-year stay at the Bernabeu.
Current skipper Sergio Ramos could depart the Spanish capital at the end of the season.
However, Real are not confident that Varane will accept their terms and are preparing for an approach from United.
Varane is first hoping to help Real win the La Liga title before deciding on his future.
Real are currently five poins behind table toppers Atletico Madrid, who have a game in hand.