The centre-half is expected to leave the Spanish giants in search of first-team football as he continues to sit behind Pepe and Sergio Ramos in the pecking order.
Newly-appointed United boss Jose Mourinho is said to be a huge admirer of the Frenchman's talents, having signed him during his time at the Bernabeu.
And now bookmakers BetStars have placed the Red Devils at 15/8 favourites to lure him to Old Trafford this summer, ahead of Premier League rivals Chelsea (5/1).
The 23-year-old is priced at 2/1 to remain at the Spanish capital next season, while European heavyweights Bayern Munich can be found at odds of 9/4.
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Manchester United favourites to sign Real Madrid's Raphael Varane
Ian Marmion, Trading Director at BetStars, said: “Having fallen behind Sergio Ramos and Pepe in the pecking order at Real Madrid, Raphael Varane looks set for the exit door.
“Top Premier League clubs have been linked with the Frenchman, but following heavy backing we’re calling a reunion with the ‘Special One’ and have Manchester United as clear 15/8 favourites for his signature.”
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