The Brazilian is one of several Monaco players being chased by some of Europe's biggest clubs after their title heroics in France last season with Inter Milan and Real Madrid also believed to be keen on the 23-year-old.
The Telegraph reported earlier this month that United were in talks to sign the player and it looks like a breakthrough has been found as the Mirror are citing a report from Corriere dello Sport that claims a deal has now been agreed between the two clubs.
Fabinho has been speaking live on Brazilian television on Friday and the channel chose to do a Q+A session where fans sent in their questions for Fabinho to answer.
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Fabinho joined Monaco in 2013 on loan from Portuguese side Rio Ave and made his move permanent in 2015, when he also won the first of four caps for Brazil.
Speaking to Esporte Interativo, he said: "It's a tempting invitation. Sure enough, I would think well about it".
Fabinho played a key role in Monaco's Ligue 1 triumph last season, and their run to the Champions League semifinals.
According to renowned Italian source Corriere dello Sport, the 23-year-old Brazilain worldwide is getting closer to signing for the Red Devils after Monaco agreed a fee worth 40 million euros ($45million) with the British side. "We like Manchester United and the work of [Jose] Mourinho, but we have a little soft spot for City", Fabinho's father Joao told French television programme Telefoot, as quoted by Sky Sports.