The Red Devils were strongly linked with De Ligt ahead of the 2019-20 campaign, but Juve ultimately won the race to sign the Netherlands international from Ajax.
The centre-back has made 27 appearances for Maurizio Sarri's side this season, but there have been suggestions that he could be on his way out of the club this summer.
According to The Sun, Ole Gunnar Solskjaer's side are interested in a potential swap deal involving Pogba, who continues to be linked with a move away from Old Trafford.
Juve are thought to be keen on bringing the France international back to Turin, and a deal could be on the cards if the Italian champions offer £30m plus De Ligt for the 2018 World Cup winner.
Pogba, who is yet to play in 2020 due to an ankle injury, will see his contract at Old Trafford expire next summer, although the 20-time English champions do have the option of activating a further 12 months.