The England international has only just returned to action following shoulder surgery in the summer, making his first appearance of the season against Leicester City last weekend.
Rashford came off the bench to score in the 4-2 defeat to the Foxes, before starting against Atalanta in the Champions League on Wednesday and again finding the back of the net.
However, he was then forced off against the Italian side with a dead leg, which the Manchester Evening News claims could rule him out of the clash with the Reds at the weekend.
When asked if Rashford would be ready for the game, Ole Gunnar Solskjaer replied: "I don't know. I hope so and I think so. It's a dead leg. Sometimes that can take longer than what you want but if we treat it well he should be okay."
Going into the match at Old Trafford, Man United sit sixth in the Premier League table, four points behind Liverpool, who are second.