Varane has just one year remaining on his contract at the Santiago Bernabeu but reportedly has no intentions to renew his current deal.
Cadena SER reports Varane has become demotivated with life at Madrid.
He has already won every major honour with the Los Blancos, including four Champions League titles, and is believed to be intrigued by the possibility of a new challenge elsewhere.
A return to France could be on the cards as Paris Saint-Germain eye a move, while Manchester United are keen on taking him to the Premier League.
The report states that Madrid have the view that a deal can be done to satisfy all parties.
They value their centre-back in the region of £60-80million but may have to reduce their asking price given they are in a difficult position with his contract.