The 28-year-old, who has less than 12 months on his current contract, is yet to agree terms over a new deal to stay at Old Trafford and he is believed to be keen on a potential move to the Santiago Bernabeu.
Marca reports that both Pogba and Paris Saint-Germain forward Kylian Mbappe are at the top of Real Madrid’s priority list for next summer, and they are hoping to lure the French internationals to La Liga on free transfers.
Los Blancos are also planning to sign Borussia Dortmund’s Erling Braut Haaland, who will see a £68m release clause become active in his contract next year.
Pogba’s agent Mino Raiola is looking to tie the midfielder down to a new lucrative contract, as the Frenchman turns 29 in March and believes his next deal will be the last major contract of his career.
If Pogba fails to sign a new deal with United before January, then he can negotiate a pre-contract agreement with another club to leave for free next summer.