Pereira played a key role for Ole Gunnar Solskjaer's team during the first half of the season but has slipped down the pecking order since the arrival of Bruno Fernandes from Sporting Lisbon in January.
The 24-year-old signed a long-term contract last summer but is keen to play regular first team football.
Solskjaer would like to keep Pereira in his squad ahead of a busy season in the Premier League and Champions League but is unlikely to give the Brazil international any assurances over his role.
Valencia, where Pereira played on loan during the 2018-19 season, and Benfica are monitoring his situation.
Solskjaer has money to spend on transfers this summer but, with the club tightening its belt during the coronavirus pandemic, the Norwegian has been told he will need to supplement the funds with the sale of fringe players.
Solskjaer wants to keep hold of Jesse Lingard and Diogo Dalot but will not make promises about first-team football after the pair played reduced roles this season. Barcelona are among the clubs interested in Dalot.