According to the Manchester Evening News, the Red Devils are busy finalising discussions with the French centre-back and his representatives ahead of a potential move.
Man United hope to complete a deal for Varane in the coming weeks as they look to close the gap on their local rivals.
Manchester City regained the Premier League title with relative ease last season, finishing 12 points clear of Ole Gunnar Solskjaer’s side.
It’s hoped that the additions of Varane and Jadon Sancho, whose move from Borussia Dortmund is all but signed off, will enable United to challenge for top spot.
Solskjaer has been keen to strengthen at centre-back, with doubts lingering over Victor Lindelof and Eric Bailly.
With his pace and pedigree, Varane is seen as an ideal partner for club captain Harry Maguire, who completed his £80million move from Leicester City two years ago.
Academy graduate Axel Tuanzebe and long-term injury absentee Phil Jones are the other established centre-backs in Solskjaer’s squad.
After ten years at the Bernabeu, during which he has collected a wealth of silverware, Real Madrid have accepted that Varane will soon be leaving.
He arrived from Lens as a teenager in June 2011 and went on to become a distinguished servant of the club, contributing to three league titles and four Champions League wins.
Varane has made 360 appearances for Real in all competitions, many of them under his compatriot Zinedine Zidane, who has enjoyed two successful spells in charge of his former club.
At international level, the 28-year-old has won 79 caps and played a key role in France’s success at the 2018 World Cup.
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