Erik ten Hag knows the 25-year-old from their time together at Ajax. However, sources have told ESPN that Ten Hag is not a particular pull for De Jong, and there is an acceptance at Old Trafford that it would be a difficult deal to get over the line.
United are in the market for a central midfielder and have been alerted to the possibility Barcelona may need to offload De Jong to fund other summer business.
Sources have told ESPN that De Jong's preference is to stay at Barcelona, but if he was told he was surplus to requirements at Camp Nou he would prefer to join a club where he would play Champions League football.
United already know they will not qualify for next season's competition after a disappointing campaign in the Premier League.
Sources have told ESPN that Manchester City are among a host of other clubs to have shown interest in the Dutchman.
Pep Guardiola is an admirer, and City were in the hunt when he moved from Ajax to Barca in 2019.
Veteran midfielder Fernandinho will leave the Etihad Stadium at the end of the season while there is also interest in Oleksandr Zinchenko leaving room in the squad for additions in midfield and at full-back.
Additional reporting from ESPN's Sam Marsden and Moises Llorens.