The Red Devils have yet to hit a new deal with Pogba, 28, whose current deal expires next summer, meaning the Frenchman can leave Old Trafford for free.
De Jong recently moved on from Camp Nou.
According to the Daily Mail, Man United are poised to join rivals Manchester City and Liverpool in the race to sign the 24-year-old, which could be available in the January transfer window.
City has previously reported an official offer worth 90 million.
De Jong, who is tied at Camp Nou until June 2026, has played 107 games in all competitions for Barcelona since joining Ajax in July 2019 , scored nine goals and delivered 14 assists.