Manchester United have been in talks with Varane over taking him to Old Trafford and the Frenchman has indicated that he is keen on the move.
The defender has not responded to the new contract offer Real Madrid have made and is claimed to have told the club that he wants to join Manchester United.
But negotiations have been complicated between two clubs and Real Madrid have rejected a first written offer for €45m from the Red Devils.
Real Madrid want Manchester United to get closer to their €70m asking price and, according to Spanish daily AS, they are ready to keep him if they do not get the right price for him.
The Spanish giants believe if Varane stays on the club will get more time to convince the player to sign a new contract.
Real Madrid do not want to give away the Frenchman at a knockdown price and are willing to stand their ground.
However, that is an unlikely scenario as the defender wants to try a new challenge and is keen on the move to Manchester United.
The negotiations are still ongoing and the two clubs are still holding talks to work out an agreement for the transfer.
Varane would have preferred to go straight into training with Manchester United but is now likely to join Real Madrid for pre-season.
