The 19-year-old striker burst onto the scene last season but had struggled to emulate that sort of form this term until a recent run of three goals in his last four games for United.
One of those came against Premier League leaders Chelsea when he started ahead of top-scorer Zlatan Ibrahimovic, and Scholes believes that the youngster would continue to pip the 35-year-old in the pecking order if Jose Mourinho had a fully-fit squad to choose from.
"He will be a brilliant centre-forward, there's no doubt about that. My only concern is because he's so quick, and United will possibly have two or three other top, top centre-forwards, that he might just get shoved out to wide areas," he told BBC Radio 5 live.
"It's not a bad thing - look at Cristiano Ronaldo's record, it's sensational. People like Neymar, he's got that kind of ability I think. It's a lot to live up to but I think he's got that in him and he can be a world star I think.
"He'd be my [first-choice] central striker now in big games. Definitely in the big games. You saw the difference on Sunday to what it did to the speed of the team. He almost occupied three centre-halves and [N'Golo] Kante trying to get back to him as well. He gives space to other people by running in behind."
With Ibrahimovic rumoured to be out for the remainder of 2017, Rashford is expected to become a more regular starter for Mourinho until the end of the season.