The 20-year-old is still waiting for a first-team debut at United but has been impressing out on loan at Belenenses.
The Portuguese youngster has made eight league appearances for the eighth-place side and now the division's leaders Benfica are lining up a swoop.
According to O Jogo, Benfica are wary of interest in their current first-choice Ederson, who has been linked with Manchester City among others.
And it has been suggested that they want to complete a permanent deal for Pereira, who they see as an ideal long-term successor.
The former Rochdale loanee is currently on a season-long loan at Belenenses but it has been reported that tentaive talks have begun with Benfica regarding a permanent switch.