The Brazil international was in impressive form for the Dutch outfit during the 2021-22 campaign, contributing 12 goals and 10 assists in 33 appearances across all competitions.
The Red Devils were strongly linked with the 22-year-old earlier this summer, with manager Erik ten Hag said to be keen on a reunion with the attacker that he managed at Ajax.
Chelsea and Liverpool have recently been credited with an interest in the Brazilian amid suggestions that Man United had cooled their interest.
However, the Mancunian giants are still firmly in the hunt for the winger and are keen to bring him to Old Trafford before the summer transfer window shuts down.
The 20-time English champions have already agreed to sign Lisandro Martinez from Ajax this summer, with the Argentine expected to sign a five-year contract with the club.