The 25-year-old, who moved to the Bernabeu from Lens in 2011, reportedly wants to find a new challenge having won 14 major honours with Los Blancos, including four Champions League titles and two La Liga crowns.
Speaking to French publication Le Parisien, the French international and World Cup winner seemed coy when asked about his plans at the end of the current term.
“I do not want to talk about my future,” Varane said. “I am not one to discuss my future publicly.”
Reports earlier this week suggested that Varane could be used as a makeweight in a deal that would see Reds forward Sadio Mane move to Madrid, while L’equipe claimed that Manchester United were leading the chase for the centre-back.
Varane, however, suggested that he is excited about the return of Zinedine Zidane, whose return to Madrid’s helm was confirmed last Monday.
“Nine months is not a long time. It was as if it was yesterday,” the defender said. “I appreciate him both as a person and as a coach. He has been very important to me.”
Madrid are third in La Liga, having been knocked out of the Champions League at the last 16 stage by Ajax.