The Portuguese boss was hoping to complete a deal for the Paris St-Germain right back, however, was turned down after the Frenchman was allegedly refused a work visa for England.
Fabinho had been previously linked with a move to Old Trafford and although he will be more expensive to secure, Mourinho is set on trying to bring in four new players this summer.
Monaco are thought to have rejected a €40m offer from Atletico Madrid for the Brazilian and Mourinho has been told the price if he wants to bring the player to Old Trafford.
He is also a fan of Mourinho and would be keen on a reunion after the Portuguese boss gave him his debut as a Real Madrid player in 2013.
Monaco have sold many of their top stars and will be reluctant to sell any more, but every player has a price and United understand how much they must pay to get Fabinho to Old Trafford.