L'Equipe says Varane is weighing up a move away from the Spanish capital.
Varane has enjoyed a trophy-laden eight years at the Bernabeu since joining the Spanish giants from Lens in 2011.
The 25-year-old centre-back has reservations about remaining in Madrid and is keen to explore his options as he seeks a new challenge.
Were Varane to become available then it would put Europe's leading clubs on high alert - including Manchester United.
The Frenchman had the chance to sign for the Old Trafford club when he left Lens in 2011, but instead plumped for a move to Madrid.