Having last week announced the £73million arrival of England winger Jadon Sancho from Borussia Dortmund, the Old Trafford giants stepped up their pursuit of the long-standing defensive target.
Ole Gunnar Solskjaer’s men are now closing in on the signing of Real centre-back Varane, having agreed a deal worth a reported £34million rising to £42million with add-ons.
The 28-year-old, who won the 2018 World Cup with France, was due to be out of contract at the Bernabeu next summer.
Varane moved from Lens to Madrid in 2011 and has made 360 appearances across all competitions since.
He has won 18 major honours during his time with Los Blancos, including four Champions League titles.
If United get the deal done, Varane will join a pool of centre-back options for Solskjaer, who can already call upon captain Harry Maguire, Victor Lindelof and Eric Bailly.