The 19-year-old has become a regular member of the United squad, as well as in the England national team, just 19 months after making his senior debut at Old Trafford.
This season, the forward has scored five goals in all competitions and tends to be rotated with Anthony Martial on the left-hand side.
Mbappe and Ousmane Dembele, who are similar ages to Rashford, secured moves to Paris Saint-Germain and Barcelona respectively in the summer, and Ferdinand thinks that the United attacker needs to prove himself in the Champions League in order to become a top player.
"You have got Dembele who has gone to Barcelona and Mbappe who has gone to PSG. Would you say Rashford is of the same ilk as them?" Ferdinand told The Mirror. "I think potentially he is as good as those guys, but they have done it in the Champions League, while he is yet to prove that.
"He has to keep proving himself, and there are so many hurdles you have to get over. These young players, we are too quick to say, 'He can be this or that'. If he keeps improving, keeps working at his game and stays in love with football, he has got as good a chance as any kid in the game to be a real success and a huge star."
Rashford could feature this Saturday when United take on arch rivals Liverpool at Anfield.