The Red Devils had allegedly been planning to move for a new central-forward next summer, but they are said to be open to making a move during the mid-season transfer window.
Memphis could be available for £4m at the beginning of 2023, as his contract with the Catalan giants is due to expire at the end of June.
According to Sport, Man United are now accelerating their attempts to sign the Dutchman, with manager Erik Ten Hag viewing him as the perfect mid-season addition.
The report adds that the 28-year-old will not make a decision until following the conclusion of the World Cup, but he is allegedly interested in a return to the Premier League.
Memphis previously represented Man United between 2015 and 2017, and made 53 appearances for the club.