The World Cup winner still has three years remaining on his contract at the Bernabeu, having been an integral part of Zinedine Zidane’s side that won three successive Champions League titles.
Despite Zidane returning though, French football agent Bruno Satin has thrown Varane’s future into doubt after a conversation with the player’s brother and agent Anthony.
“I spoke recently with Anthony, and we discussed a little bit about the state of the market, so to speak,” Satin told Late Football Club.
“I think at this moment in his career he is having a profound reflection, I don’t think he has fully decided to leave Real Madrid, but he is thinking about it because he has won everything that you can at Real.
“He feels like he has the feeling that he has done what was to be done over there, and there could be a new cycle.
“Aside from that, I have not spoken directly with Raphael myself.”
Zidane reiterated his desire to retain Varane for next season, insisting he seems "fine."
"I want him to stay. We don't want a Madrid without Varane," Zidane said. "He's also young. He seems fine and he hasn't told me otherwise, which is what's important."
Varane has made 268 appearances since joining Madrid in 2011, scoring 12 goals.
But as Zidane attempts to revitalise his squad this summer, Varane may push for a move.
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies