The Brazilian midfielder was one of the star performers for the French club last season after helping them win the Ligue 1 title and reaching the semi-finals of the Champions League.
Fabinho can operate in a number of positions including central midfield, right back and a wing-back and his versatility will appeal to the United manager after making over 50 appearances last season.
After securing the signing of Victor Lindelof from Benfica, Mourinho is keen to get his business done in the transfer market as quickly as possible and reports in Italy suggest a move for Fabinho is close to being completed.
Leading Italian newspaper Corriere dello Sport claim United have agreed a deal which is close to €35million and has a €5m bonus linked to goals and appearances.
Fabinho is also being chased by Juventus and Inter Milan but it appears United have won the race to sign the 23-year-old and a deal could be announced in the near future.
Mourinho means business this summer and is also determined to bring in a big name forward.
Real Madrid’s Alvaro Morata continues to be linked with a move to Old Trafford and after missing out a deal to sign Antoine Griezmann, the United boss remains confident he can strike a deal to sign the Spanish striker.