The 18-year-old striker has impressed in United’s junior sides this season, scoring three times at Under-19 level and also finding the net regularly for the Under-21 team.
His breakthrough into the senior side, though, has surprised even the most optimistic of United supporters, with four goals in his first two games.
Having struck twice in a Europa League win over FC Midtjylland last Thursday, Rashford followed that up with two more in Sunday's 3-2 Premier League victory over Arsenal.
Manager Louis van Gaal is wary of asking the Manchester-born forward to take on too much responsibility too soon.
Van Gaal said on Tuesday (Mar 1) he will have no problem keeping Marcus Rashford’s feet on the ground after his remarkable start to life at the club.
It means that Van Gaal will have a tough job leaving the teenager out, even as Anthony Martial nears a return to fitness after a recent hamstring injury.
United’s manager is also concerned about the level of media attention that Rashford is facing, but is adamant that the striker is level-headed enough to deal with it.
“First, I think that the media have to let him in peace and rest,” Van Gaal told press at United’s Carrington training base.
“You are in front of his house and that kind of stuff. I don’t think that is beneficial for a boy of 18. Give him time to be 18. We shall guide him in that way.
“I think he’s a very modest guy so I don’t think that will be a problem. When you have so much media attention, it can go another way, but I feel he can keep his feet on the ground.”
United have had a troubled season, but are on the up again after successive victories across three competitions, and looking to revitalise their challenge for a Champions League place.
Van Gaal’s touchline antics have attracted as much attention as their recent improvement.
The Dutchman theatrically dived to the floor in front of fourth official Mike Dean when a decision went against his side during their 3-2 win over Arsenal on Sunday (Feb 28).
It harked back to his early managerial career, when he performed a flying kung fu-style kick on the touchline after his Ajax team were denied a penalty during the 1995 Champions League final against AC Milan.
At that time, Van Gaal was furious that Milan midfielder Marcel Desailly had escaped unpunished after a head-high tackle on Ajax striker Jari Litmanen.
The manager has adopted a more measured approach on the touchline in recent years, and has occasionally been criticised for lacking passion.
He insists that he does care, but has no plans to continue being demonstrative on the touchline, because he does not wish to be branded a “clown”.
“It’s not a part of my philosophy,” he said. “I am not a clown. I am Louis van Gaal. I am a human being and a manager.
“My players have to think on the pitch. I help them more to train what I have said [so] that they see the solutions on the pitch. That’s why I’m not doing that.
“I have done this also in the Champions League final. I was jumping like that also when there was a defender who was putting his foot at that height against Jari Litmanen.
“That was my way of saying it, but it was too emotional. You have to deal with the fourth official and the authority of the referee.
“I have to control my emotion and that is why I have apologised. But I don’t feel sorry for it, because it’s me. I think I was right.”