The midfielder has just completed a loan spell with Lazio.
He could be loaned out again for next season, but it's understood that Pereira would like a clean break from United, with his playing time likely to be very limited if he does remain at Old Trafford.
Pereira only managed one goal and four assists in 33 appearances in all competitions for Lazio. And the Rome-based club are unlikely to exercise the option, including in the loan deal, to buy the player for €27 million.
It's understood there is interest from clubs in Spain and Italy this summer, with Pereira's United contract expiring in two years.