The Brazilian's versatility, being able to play at right-back as well, is another factor as Mourinho wants to improve in that position with Antonio Valencia being a natural winger.
Fabinho, who is valued at €35m (£30.7m), has already revealed that he would be open to working under Mourinho again, having briefly worked under the Portuguese manager during his time at Real Madrid.
"He is an excellent manager. No doubt," the 23-year-old said. "If Mourinho invites me [to join United], it would be very tempting, but, first of all, I would have to talk with my agent and with Monaco to make the things right."
"But Manchester United is a great team, and I would think about it, for sure."
As for Matic, the Serbian is set to become the Red Devils' second major signing of the summer after Victor Lindelof as the midfielder will reunite with the 54-year-old for a fee in the region of £35m ($44.8m).
Matic was signed by Mourinho in 2014 as the former Benfica man rejoined Chelsea and notably won two Premier League titles in three seasons.
His replacement at Stamford Bridge is expected to be another Monaco player in Tiemoue Bakayoko, who is close to completing a £36.7m ($46.8m) move.
The imminent transfer of the Frenchman along with United's continued pursuit of Fabinho and the race for Kylian Mbappe represent more blows to the Ligue 1 champions who have already lost the likes of Bernardo Silva, Valere Germain and Nabil Dirar following a successful 2016/17 season.