Martial has struggled to earn a regular spot in the lineup at Old Trafford this season, starting just one game so far in the current Premier League campaign.
According to 'Mundo Deportivo', Barcelona are monitoring the winger's situation at United and believe he can make an impact at the Camp Nou.
The Spanish giants are searching for a player who can control the left-wing, with Denis Suarez and Gerard Deulofeu failing to live up to expectations under Ernesto Valverde.
Record signing Ousmane Dembele picked up a hamstring injury last month and could be out for up to three and a half months, and Barca see Martial as a player who can fill the void left by the former Borussia Dortmund man.
Despite falling down the pecking order at United, Martial has impressed whenever given the chance, mainly in cup competitions. The Frenchman has scored five goals and assisted six times so far this season.
Barcelona are hoping uncertainty over a starting place at Old Trafford will be enough to convince Martial to make the switch to Barcelona sooner rather than later.