The pair have been handed the task of leading United's line this season after Romelu Lukaku's departure.
They have scored two goals each from the opening two games, and Martial says the competition between them is benefitting Ole Gunnar Solskjaer's side.
"At training, we have this competition between us about scoring goals," Martial told Sky Sports. "We measure who does the best finishing and who scores the most.
"Who's winning? Well, that depends... Sometimes it's him, sometimes it's me. In games, Marcus likes to play in the middle, like me. I don't mind dropping off, dropping out, we interchange during games.
"It doesn't bother me to let him take the lead occasionally. It helps us to terrorise opposition defences and I hope we can keep it up over the course of the season."