Agent Mino Raiola has announced his intention to find a new club for Pogba, who will not sign a new contract at Old Trafford according to the Italian.
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The Frenchman has a contract with United until 2022 but Raiola has invited bids for the 27-year-old in January and next summer.
Pogba's preference is to join Madrid but sources have told ESPN that United do not believe the Spanish champions can afford a significant transfer fee and the midfielder's hefty wages of around £290,000-a-week.
Pogba is a favourite of Madrid coach Zinedine Zidane but there are question marks over the 48-year-old's job at the Bernabeu after a mixed start to the season.
Juventus and Barcelona have also expressed interest in signing Pogba in the past but, like Madrid, have been forced to tighten their finances following the coronavirus pandemic. Paris Saint-Germain is Pogba's only other viable option.
Because of lack of funds available for transfers, sources have told ESPN that United are expecting to receive cash plus swap offers but they will not consider players not already on the recruitment department's list of targets.
Sources have told ESPN that given United's financial stability in comparison to some of their European rivals, the possibility that Pogba could eventually sign a new contract has not been ruled out, although top bosses are split on whether it is in the best interests of the club to keep hold of a player who has indicated more than once that he wants to leave.
United are determined that they will not be bullied into accepting a low bid for Pogba -- signed for a then world record £89.3 million from Juventus in 2016 -- in January or next summer, by which time he will have just one year left on his contract.