La Gazzetta dello Sport in Italy has claimed that Fabinho will be Manchester United's second summer signing.
The article claims that the two clubs have reached an agreement for £30million and the player will be announced in the coming days.
Internazionale and Juventus in the Serie A were also interested in the 23-year-old defensive midfielder.
Meanwhile, the player has confirmed that a move to Manchester United is "very tempting".
"Manchester United is a great team and I would think about it," he told Brazilian television channel Esporte Interativo.
"If [Manchester United manager Jose] Mourinho invites me it would be very tempting.
"But I would have to talk with my agent and Monaco to make the things right."