The 23-year-old was a key player in the French club's title-winning campaign last season, which was their first success in the league since 2000. Leonardo Jardim fielded Fabinho at right-back at the start of the season before the Monaco manager then changed the Brazil international's position and moved him to the midfield, where he excelled.
His form saw him attract interest from top clubs across Europe, including both the Manchester sides.
The former Real Madrid starlet played under Jose Mourinho when the two were at the Spanish capital club together in 2013. His name was included on a list of targets for both United and Pep Guardiola's side ahead of the summer transfer window.
Earlier this month, it was reported that the player was close to joining the Red Devils and was expected to be their second summer signing following the arrival of Victor Lindelof from Benfica. However, IBTimes UK revealed on 23 June that Fabinho was not close to joining the 20-time English champions.
Despite interest from both United and City, Fabinho is now unlikely to make a move to England. Monaco's league rivals Paris Saint-Germain have also registered interest in signing the versatile South American and a switch to Parc des Princes from Monaco could be a possibility this summer.
Mourinho was keen on bringing Tottenham Hotspur's Eric Dier to Old Trafford but the north London club are unwilling to sanction the England international's sale - forcing United to look elsewhere in the transfer market.
Chelsea midfielder Nemanja Matic has also emerged as a target for the Red Devils. A move for the Serbia international looks like a possibility and the Blues are willing to sanction the sale for a player they value at around £40m ($50.9m)