Louis Van Gaal, Manchester United manager might jump at the chance of signing the highly rated French defender.
Real Madrid are aware of the number of top clubs that have shown interest in the French international.
As per The Express report, Chelsea and Manchester United have been told to pay £20 million if they are interested in signing Varane.
Both the teams are capable of buying the player at the mentioned fee, but it also depends on which team would Varane prefer, if the choice boiled down to the French youngster.
It would not be an easy task for Varane to straightaway walk into Chelsea's starting line up, where Gary Cahill and John Terry form the backbone of the team's defensive unit and Mourinho is someone who does not prefer to tinker the starting eleven too much.
Hence, if Varane decides to choose Stamford Bridge over Old Trafford, the player may have to wait for his turn and deliver the goods to cement his place in Mourinho's team.
But, with Mourinho already having known the player from his Real Madrid managerial days, it would not take much time for the Madrid star to settle at Stamford Bridge.
Though, considering a switch away from the Bernabeu and warming the bench at Stamford Bridge is something Varane might not be pleased with.
Considering Varane being a young defender, who wants more game time, he could be a perfect fit for Manchester United, who does not seem to have a settled back line, hence leading to many problems at the back.
If Varane does decide to leave the La Liga giants, his only reason could be lack of first team football, which he is not getting under Carlo Ancelloti in Real Madrid.
While Manchester United have tried different set of defensive pairing, they have not been able to solve their defensive woes and their injury worries have not made the situation any better.
The French international could bring stability into Manchester United's back four. Standing 6 feet 3 inch tall along with his good physique makes his game perfectly suited to the demands of the English Premier League.
Along with his physical structure, he is good with the ball on his feet and reads the game beautifully, like great defenders of the past, who were technically correct.
Manchester United have been interested in signing the Aston Villa defender, Ron Vlaar for some time now, but acquiring Varane's services could be a major upgrade to United's defense line.