Any deal for the France centre-back would likely involve United keeper David De Gea moving in the opposite direction.
Real are willing to splash £60million on the Spain star as they look to make amends for their disastrous attempt two years ago.
A last-minute issue with paperwork between both clubs scuppered a move for De Gea, 26, in September 2015.
Real Madrid consider Raphael Varane indispensable and part of their futureGetty ImagesRaphael Varane is reportedly in talks with Jose Mourinho over a Manchester United moveGetty ImagesAlvaro Morata is another Real Madrid star wanted by Jose MourinhoGetty Images
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While Los Blancos would consider giving up Morata, who they value at over £50m, they are likely to reject Mourinho’s demands for Varane.
The La Liga giants consider the defender indispensable and a key player in the future.
Mourinho has struggled to cement a defensive partnership in his debut United season.
Any deal for Raphael Varane would likely involve David De Gea moving to Real MadridReuters
Eric Bailly, a £30m summer signing from Villarreal, is a regular for the Red Devils, but question marks remain over the remaining position.
Marcos Rojo has filled in well this season but Mourinho prefers to play him at left-back when possible.
Chris Smalling and Phil Jones have both missed too many games through injury, while Daley Blind – who Louis van Gaal often used at centre-back – has fallen down the pecking order.
Eric Bailly has been a regular under Jose Mourinho, but Marcos Rojo is preferred at left-backPA:Press AssociationChris Smalling and Phil Jones have both suffered with injuries this seasonEPA
Meanwhile, United appear to be preparing for life without De Gea.
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