The Portuguese midfielder only joined the Ligue 1 side over the summer as a part of their ambitious plans, but the Red Devils are confident that they can tempt him away with the promise of becoming one of their key men.
Moutinho was heavily linked with Tottenham prior to his move to the Stade Louis II a matter of months ago, and has long been thought of as one of European football’s top passers.
Rumours have been circulating that a number of Monaco’s new arrivals have grown disillusioned at the club – chiefly Radamel Falcao – which has alerted United boss Moyes.
The Scot is desperate to spend big in a bid to save his debut season at Old Trafford, and is thought to have around £100m at his disposal to do so.
Moutinho is one of a number of targets, with the former Porto man seen as the ideal player to inject some creativity into the Premier League champions’ ranks.
The likes of Namanja Matic, Ilkay Gundogan and Yohan Cabaye are also believed to be on the club’s radar.