Reports in Spain this month claim the Frenchman wants to leave the Spanish capital to test himself elsewhere.
Madrid beat United to Varanes signature in 2011 thanks to the intervention of Zinedine Zidane but the Red Devils have never given up hope of signing the 25-year-old.
Centre-back had been a position of priority for Jose Mourinho but Ole Gunnar Solskjaer has improved his sides defence and would prefer to strengthen other areas of the squad.
Part of Uniteds refusal to bow to Mourinhos demands last summer when he wanted to sign the likes of Harry Maguire and Jerome Boateng was that the right calibre of player was not available on the market.
Varane is viewed as a world class acquisition and the Evening Standard claim United would be prepared to pay £100million to sign him this summer.
However, the club will not waste time trying to persuade the Frenchman moving to Old Trafford and the move is dependent on Varane indicating that he wants to leave the Bernabeu.
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