Pereira, 24, has made 40 appearances in all competitions this season, including 18 Premier League starts.
However, after the resumption of play in England, Pereira was given only 62 minutes of game time by Solskjaer.
And Pereira wants to join a club where he will have a better chance of starting matches every week.
Solskjaer had hoped the Brazilian midfielder would stick around and tried to convince him, but his efforts were in vain.
Pereira’s agent, Kia Joorabchian, is already in talks with clubs from Portugal, Spain and Germany over a potential move.
In the 2017-18 season, Pereira had a good loan spell with Valencia and club president Peter Lim would welcome his return.
Pereira joined United in 2012 when he was just 17 and has made 75 appearances in total for the Red Devils.
His current contract expires in June 2023 with United having the option to add an extra year.