Varane, 21, joined Real from Lens in 2011 and is third-choice centre back behind Spain's Sergio Ramos and Pepe of Portugal.
He has made 11 appearances for France and was part of the squad at the World Cup finals in Brazil, where Les Bleus lost 1-0 in the quarter-finals to eventual winners Germany.
(Reporting by Iain Rogers, editing by Ed Osmond)
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