Fabinho was linked with a switch to Old Trafford last summer but a move failed to materialise, although the Red Devils are thought to be interested in bringing the versatile midfielder to the club in the 2017 summer transfer window.
The 23-year-old can play as a right-back or a defensive midfielder.
Fabinho only moved to Monaco permanently in 2015 having been on loan at the Stade Louis II in 2013, from Portuguese club Rio Ave.
United will be keen to bolster their squad this summer with plenty of competition among the top teams and a Champions League campaign to think about.
The Swedish centre-back moved for around £30.8m, while names such as Alvaro Morata, James Rodriguez and even Cristiano Ronaldo continue to be linked with Old Trafford. United are among those linked with the Brazil global, who told Esporte Interativo in his homeland that he would be open to an approach.
"But I would have to talk with my agent and Monaco to make the things right".
Fabinho made 37 Ligue 1 appearances last term, scoring nine goals for Leonardo Jardim's champions. The Brazilian is also a transfer target of Juventus although the Serie A giants are set to miss out on his signing given that they only have one slot available for non-EU player and that they are planning to fill it with either Douglas Costa or Danilo.