He is set to become United manager Louis van Gaal's sixth signing of the transfer window before today's 6pm deadline passes.
Bastian Schweinsteiger, Morgan Schneiderin, Sergio Romero, Memphis Depay and Mateo Darmian have all come through the doors at Old Trafford over the summer months.
United were also expected to sign winger Pedro from Barcelona before Chelsea swooped in on the deal at the last minute.
Anthony Martial - Spotlight on
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As for Martial, the Frenchman boasts over 50 appearances for Monaco since making his debut in the 2012/13 season.
Last term he scored nine Ligue 1 goals for the club, who failed to qualify for the Champions League this time around.