Fabinho, 23, has been heavily linked with a move to Old Trafford this summer as Jose Mourinho looks to bolster his ranks ahead of next season.
The Portuguese boss wants to get his transfer business done early and has already got the ball rolling with the signing of Victor Lindelof from Benfica.
But he has identified the defensive midfield as an area for improvement as he wants to allow Paul Pogba to push further forward.
The Brazil international admitted this week that a move to Manchester United would be “very tempting”.
And Italian journalist Gianluca Di Marzio reckons the Premier League giants have now stepped up their pursuit of Fabinho.
It is said the Red Devils have tabled a £44m bid for his services and talks are underway about a possible transfer.
Fabinho established himself in his new role as a defensive midfielder at Monaco, having been converted from right-back.
And his exploits helped them seal the Ligue 1 title for the first time since 2000 and reach the Champions League semi-finals.
But Fabinho has hinted if United tabled a bid for him he would consider leaving France.
He told Brazilian TV station Esporte Interativo: “The offer would be tempting, first I would talk with my agents/representatives and with Monaco to make sure the right decision is made.
“But it’s a great team and I would definitely think hard about the offer.”
Fabinho is contracted to Monaco until 2021 and is one of several players who could leave the French side this summer.
Benjamin Mendy, Kylian Mbappe, Thomas Lemar and Bakayoko have all been linked with moves to top clubs.
Bernardo Silva has already completed a switch to Manchester City where he signed a five-year contract in a deal worth around £43m.
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