Mourinho wants to bring a holding midfielder into his squad and has been strongly linked with a move for the Brazil international.
But according to the Manchester Evening News , it is understood that he will not persue a deal for Fabinho and could make a move for Chelsea midfielder Nemanja Matic or Tottenham star Eric Dier.
Fabinho was outstanding for French champions Monaco last season and has emerged as one of the most sought-after players in Europe.
He is expected to be one of a host of stars to exit Leonardo Jardim’s side, along with Bernardo Silva, Benjamin Mendy, Tiemoue Bakayoko and Kylian Mbappe.
But United sources insist they are not in the race for the 23-year-old as Mourinho seeks a long-term successor to Michael Carrick.
Despite being represented by Mourinho’s agent Jorge Mendes, Fabinho is not seen as one of the four key signings Ed Woodward has been tasked with the responsibility of securing.
United’s executive vice chairman is working through a wanted list that includes a central defender, central midfielder, winger and striker.
He has already agreed a fee of £30.7m for Benfica centre-back Victor Lindelof and is hoping to wrap up the signing of Real Madrid striker Alvaro Morata.
Mourinho is determined to land a holding midfielder, capable of helping Paul Pogba realise his full potential.
Carrick has been handed a new one-year deal at Old Trafford. But Mourinho wants a long-term anchor in the heart of midfield, in the fashion of Claude Makelele and Matic, who were pivotal to his three titles as Chelsea manager.
Any move for Matic relies on Premier League champions Chelsea’s willingness to sell to a direct rival.
Antonio Conte’s pursuit of Bakayoko could prove decisive in facilitating a move.
The arrival of the French international could push Matic to the fringes at Stamford Bridge, with double player of the year N’Golo Kante now considered the driving force in midfield.
While Chelsea would prefer not to sell to a Premier League rival, an offer in the region of £40m could tip the transfer in United’s balance.
United secured the signing of Juan Mata from the West Londoners in January 2014.
At that time Chelsea’s preference was to see the Spanish playmaker go overseas – but the £37.1m on offer from Old Trafford was too good to refuse.
It’s believed Matic is also open to a move to United and remains ahead of Fabinho in Mourinho’s thinking.