Lionel Messi pipped Virgil van Dijk to last year’s prize, with attacking players historically preferred to win the gong.
This sentiment has led Danny Murphy to believe Trent Alexander-Arnold is unlikely to ever win the award because he is a right-back.
But that same reasoning means Shaw reckons Rashford has a good chance of securing the coveted prize in the future.
“Yeah, for sure [Rashford can win a Ballon d’Or],” Shaw told Manchester United’s official website. “He’s improved greatly from when he first came on the scene, not just on the pitch, but off the pitch as well.
“He’s matured so much. He’s really turned into a man and I think everyone’s seen the way he’s conducted himself off the pitch; especially during this pandemic, he’s been unbelievable.
“He’s a massive example to everyone. He’s matured so much and a lot of credit for that goes to him and also to his family, who have kept him very grounded.”
He added: “He’s a big inspiration for a lot of young people, especially the ones who are coming through from Manchester.
“In Marcus, they’ve got someone to look up to not just on the pitch but off it too, which is really nice to see.
“As a player, he’s improved so much but he always wants to learn, always wants to get better and, to me, he’s getting better every time I see him play.
“He’s looked unstoppable at times this season and he’s looked so confident. I haven’t seen that in him before. He was always confident, but not to this level, and he’s matured so much.
“He knows he has the ability to be one of the best and he’s pushing himself all the time to maximise that. There’s no reason why, if he keeps going, keeps pushing himself, that he can’t win it one day.”