The 26-year-old was expected to join the Brazilian club on a permanent basis at the end of his season-long lease.
But Pereira has not done enough to convince Flamengo to spend £ 12 million on him and he has few other offers on the table.
Ten Hag worked with Pereira when he was still a teenager at PSV Eindhoven, and he remains an admirer of the midfielder.
Should Flamengo decide not to buy him, ESPN reports that Ten Hag wants Pereira back at Old Trafford, and John Murtough, the club’s football director, has told the midfielder that the Ajax boss wants him back at Dreams Theater in that scenario.
United are ready to lose Paul Pogba and Nemanja Matic on a free this summer when their contracts expire, while there are also doubts about Donny van de Beek’s future.
It will leave the club easily in midfield and Pereira can provide back-up to Fred and Scott McTominay, though Ten Hag also want to sign on at least one replacement.
United are set to give Ten Hag between £ 100m- £ 150m to spend this summer, but he can supplement his budget through player sales.
Aaron Wan-Bissaka, Phil Jones, Eric Bailly, Anthony Martial and Alex Telles are all available, with United willing to listen to offers for the five players.
Dean Henderson is another potentially valuable asset and the Englishman is keen to leave in the hunt for first-team football.
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