The France international moved to Spain from Lens in 2011 but has seen his time at the European champions blighted by knee injuries.
After making a solid start to his career in La Liga, the 21-year-old underwent knee surgery at the end of the 2012-13 season and struggled again during the previous campaign.
He made his return from injury towards the end of the term and started in their 4-1 extra-time victory over Atletico Madrid in May's UEFA Champions League final.
Varane has made 71 appearances for Real in all competitions since arriving and has featured in three games this season, making his solitary start in a 1-0 Supercopa de Espana defeat to Atletico last month.