The Red Devils reached an agreement with Juventus over a £15 million fee last week and were left to negotiations with the 27-year-old and his mother Veronique, who is his agent.
Rabiot expected a higher offer from United, who have spent the summer transfer window hunting for an 'elite' midfielder.
According to the Manchester Evening News, the move has now collapsed.
Rabiot has one year remaining on his deal with Juventus and will likely command a higher salary as a free agent in 2023.
David Ornstein of The Athletic reports the deal could be revived but it is looking highly unlikely and United have moved on to other targets.
He went on to claim 'live talks' are taking place for other options, including Real Madrid stalwart Casemiro.
The 30-year-old is regarded as one of the world's top holding midfielders, winning five Champions League titles and three La Ligas during his nine-year stint at the Santiago Bernabeu.
Marca claim the Brazil international is an option with nobody in the Spanish capital able to escape 'market movements.'
Brighton and Hove Albion youngster Moises Caicedo is said to have been offered to United but there is no official contact as of now.
Caicedo joined Brighton in 2021 after initially being close to joining United for £4 million in 2020.
He scored in last season's 4-0 win over United and dominated the middle of the park in this campaign's 2-1 opening weekend win.
So far, United have added Tyrell Malacia, Christian Eriksen and Lisandro Martinez to their squad but need more.
They finished sixth with their lowest-ever points tally in 21/22 and six first-team players departed upon the expiry of their contracts.
Cristiano Ronaldo's future remains a hot topic too and he's still desperate to leave Old Trafford for a second time.
United denied reports over the weekend which stated they were considering terminating the five-time Ballon d'Or winner's contact unless his attitude improved.
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