Martial is set for scans this week after suffering an injury to his left thigh during the 2-1 defeat to Crystal Palace at Old Trafford on Saturday.
The Frenchman was barely able to move during the final few minutes but stayed on the pitch until the end because manager Ole Gunnar Solskjaer had no more substitutions available.
Martial was limping heavily as he left the stadium and the 23-year-old, who has scored twice this season, will undergo tests this week as the club's medical staff attempt to assess the damage.
It is a blow to Sanchez's hopes of joining Inter before the European transfer deadline on Sep. 2.
The Italian side are trying to negotiate a loan deal for the Chilean with an obligation to buy next summer which would see United pay a portion of his £391,000-a-week wages this season.
Sources have told ESPN FC that the two clubs are yet to find a breakthrough in talks and the injury to Martial has complicated matters further with Solskjaer becoming concerned at a lack of options up front.
Sanchez is yet to feature this season as he continues his recovery from a hamstring injury but his exit would reduce Solskjaer's options even further ahead of a busy season in the Premier League and the Europa League.
Sanchez has managed just five goals in 45 games since arriving from Arsenal in January 2018.
Marcos Rojo could also leave Old Trafford before the European deadline. He is yet to make the match day squad in United's first three games of the season and sources have told ESPN FC that Marseille, Monaco and AC Milan are interested in signing the defender.