The Red Devils are extremely keen on signing Varane this summer, after the defender refused to sign a contract extension with Los Blancos, with his existing deal expiring next year. Ole Gunnar Solskjaer wants to add a defensive partner for Harry Maguire, and believes Varane is the ideal addition to his squad.
Van de Beek, meanwhile, has struggled for game time at Old Trafford following his £40m move from Ajax last summer, playing less than half of United's Premier League matches, and scoring just once.
And according to the Daily Star, Madrid want United to include Van de Beek in the deal for Varane on an initial loan deal and an option to buy the 24-year-old next summer.
Van de Beek was strongly linked to Madrid when he left left Ajax last summer but the 24-year-old opted to pick a move to Old Trafford instead. The report goes on to add that Varane will be available to United for £50m, and they have a chance to get the unwanted Van de Beek off their books too.
Van de Beek has been urged to leave Old Trafford by a number of pundits due to his limited game-time. Former Netherlands international Rafael van der Vaart, for example, said last month: "He fit perfectly into the Ajax system, but he doesn’t fit at Manchester United.
"If nobody leaves United [this summer], he will be lucky to get in the starting line-up. He is far too good to sit on the bench for two seasons. He needs minutes very quickly. He is still young, but time flies. A club like Borussia Dortmund would have been a better step for him. Manchester United might be a step too far for him."