The Old Trafford club triggered a one-year extension to Pogba’s contract on Friday, tying him to the club until 2022.
However, a report in the Sun suggests that the France international could be allowed to make the move to the Bernabeu that he has openly courted in the past.
Valverde is said to have been on United’s radar for a long time and the Red Devils are looking into a potential swap deal.
The 22-year-old Madrid star currently has a mammoth £640 million buyout clause in his contract.
But Pogba, who became the world’s most expensive player when he returned to Manchester from Juventus in an £89 million deal in 2016, could be included to find a deal that suits all parties.
Merengues coach Zinedine Zidane is an admirer of the 27-year-old, and Pogba has said it would be a “dream” to play for the Spanish giants.
The central midfielder had an injury-interrupted season in 2019/20, making just 22 appearances.
Uruguay international Valverde, meanwhile, has become a regular fixture in Zidane’s side this season and already has 74 first-team appearances for Real Madrid to his name.
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