United will demand €150m for the France midfielder, according to Marca.
Pogba arrived from Juventus in 2016 for €114m, making him the most expensive player in the world at the time.
Mino Raiola, the agent who will be making millions from any deal, has been informed that United plan to make it very difficult for the 2018 World Cup winner to leave.
Pogba, who scored two penalties against West Ham at the weekend, is believed to be warming to the idea of playing for Los Blancos under his compatriot, Zinedine Zidane.
However, Real Madrid have a number of high-profile targets and are reportedly assessing which deals they can afford to splash out on this summer.
If United hold firm, Madrid may be forced to back off Pogba for now.
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