ESPN says United believe Madrid are now ready to negotiate a deal for Varane, whose deal expires next summer, and are confident he could be available for around £43m.
Los Blancos had initially valued him at around £60m, a price that had put United off, but they are willing to lower their asking price in order to help new boss Carlo Ancelotti rebuild, it claims.
Varane is said to have rejected Madrid's offer of a new deal last week, with the player is reportedly unhappy that Real chose to negotiate with Luka Modric, Lucas Vazquez and Sergio Ramos ahead of him.
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