The France international has been linked with a move away from the Santiago Bernabeu this summer after failing to nail down a place in Carlo Ancelotti's starting XI.
Chelsea and United are both believed to be interested, but new boss Rafa Benitez apparently has no plans to sell Varane.
Italian media outlet Tuttomercatoweb claims that the youngster is now seen as an indispensable member of the squad, and will be paired alongside Sergio Ramos in a new-look defence next season.
The news will come as a huge blow to Chelsea and United, who had both been hoping to lure Varane to the Premier League with the offer of first-team football.
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Raphael Varane looks set to remain at Real Madrid
The 22-year-old has already made 117 appearances for Los Blancos following a £7million move from Lens in 2011.
And despite his age, Varane has laid his hands on a number of major trophies, including one La Liga, one Copa del Rey and one Champions League.
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