Varane is expected to complete at medical with United soon and join Jadon Sancho as off-season signings, while rumours swirl about Paul Pogba’s future.
It has been widely reported that United and Real have agreed to the deal, which included add-ons.
France international Varane has been with Real since 2011, making 360 appearances for Los Blancos.
He would bolster United’s backline, likely playing alongside Harry Maguire in the heart of defence, with Victor Lindelof and Eric Bailly back-up.
United were Premier League runners-up last term under Ole Gunnar Solskjaer but have not won a trophy under the Norwegian.
The Red Devils were the second top scorers in the top flight last term, behind only champions Manchester City.
But United conceded 44 goals, which was the fifth best defence in the league, behind City, Chelsea, Arsenal and Liverpool.
United legend Rio Ferdinand said on YouTube: “When you watch him sometimes he almost purrs, he’s got that pace, that poise.
“We’ve signed a genuine world-class centre-back. His list of honours is ridiculous, it’s as long as my arm.”