The Frenchman has enjoyed his best scoring season for the Red Devils, after getting the central striker role.
And Grant thinks Martial can do even better, and is always working to unlock the attacker's talent in training.
"We have a nice little battle actually," Grant said of Martial on the UTD Podcast.
"I'm always on at him in training, always digging at him in training to try to do better.
"If Anthony shoots and I save it, I go: '1-0, Anto'. Then he'll get this glint in his eye and the next one, it won't matter if the gaffer says don't worry about the shot in the end, he'll come through and want to shoot in a one-on-one.
"He won't even say anything, he'll just do that [1-1], and then the next one, and we'll do that all day. So a lovely little rivalry goes on between us.
"You might have caught it with the goal he scored at home against Bournemouth. He cuts inside and hits an unbelievable strike, then looks up in the stands at me, like that. I'm stood up giving applause, it's the type of thing to do, but he'd have loved to score that goal against me, probably more than he would do against Bournemouth!"