Pereira has only made one first-team appearance for United - as a substitute against Wigan Athletic earlier this season - but he is highly regarded by manager and compatriot Jose Mourinho.
The 20-year-old will start United's final Premier League match of the season against Crystal Palace on Sunday but according to A Bola, Benfica hope to make it his one and only start for the club.
It has been suggested that they have identified Pereira as a potential successor to Emerson, who has been linked with a move away from the Estadio da Luz.
Pereira has only made 16 appearances in senior football - with all but one of those coming at Rochdale and Belenenses - but the Portuguese giants appear willing to place faith in the youngster.
It has previously been reported that Pereira will be offered a new contract at Old Trafford.