Sanchez is well into the final year of his current deal with the Gunners and, with no sign of an end to their impasse in negotiations over a new contract, the Chilean looks certain to leave the Emirates Stadium on a free transfer next summer.
Arsene Wenger could even decide to cash in on Sanchez during the January transfer window, and The Mirror claims that the Frenchman has identified Martial as a possible replacement.
The 21-year-old has started just one Premier League match for the Red Devils this season, being largely limited to appearances off the bench otherwise.
The winger is also understood to prefer playing in a central role, which would be more likely at Arsenal rather than United due to the presence of Romelu Lukaku at Old Trafford.
Martial has scored five goals and set up six more in nine appearances across all competitions this term, though, and United boss Jose Mourinho is unlikely to be willing to sell the youngster to a direct Premier League rival.
The France international has scored 30 goals in 100 games for United since joining the club for £58m in 2015.