Martial is struggling with a hamstring issue after coming off as a late substitute in United's 1-0 win over Burnley on Tuesday night, which sent Ole Gunnar Solskjaer's side three points clear at the summit.
Solskjaer said that Martial was one of several players who will face a late fitness test over the weekend before taking on Jurgen Klopp's champions.
"I'm going to give everyone another day," he said. "Anthony is not out of it, the only ones certainly out are Brandon [Williams] and Phil Jones, they're the two that definitely can't make the game.
"A couple of others are maybe doubts. We’re hoping, fingers crossed."
Solskjaer dismissed the suggestion that United face Liverpool at a good time, despite their recent patchy run of form and the absences of centre-backs Virgil van Dijk and Joe Gomez.
"We have as many injuries as them," he said. "That's just how football is. You get injuries, that's part and parcel of the game.
"I'll give everyone tomorrow a chance to prove their fitness. There's a couple of knocks we got at Burnley that I'm not sure about but form gives us confidence.
"They are the champions, they've earned the right and we're hunters. You want something they've had. Our mentality will be to work hard to be humble to do our best and see what we can get out of the game."