The Frenchman has a year left on his existing contract and is yet to start discussions with Los Blancos over a new deal. The 28-year-old has been an important part of Zinedine Zidane's side this season, having started all but five of their LaLiga and Champions League matches.
According to Spanish news outlet Mundo Deportivo, Varane remains unconvinced about staying at the Santiago Bernabeu, and Thomas Tuchel's side are willing to pay his transfer fee to bring him over to England at the end of the current season.
The report claims that Madrid need to raise funds for the expected arrival of David Alaba and if they want to try and land Kylian Mbappe too, and will be open to selling multiple players once the transfer window opens.
Manchester United and Paris Saint-Germain have also been credited with an interest in Varane, who has hinted that he prefers a move to the Premier League. United failed to sign the defender in 2011, and were unsuccessful in luring him to Old Trafford two years, but could return this time with a lucrative offer, as long as it doesn't draw them into a bidding battle with Chelsea and PSG.