The England international made the comments during a meeting with Manchester United supporters at Old Trafford's Ambassadors' Lounge, reflecting on his time alongside Yamal at Barcelona.
Rashford spent the previous season with the Catalan club and said he had been struck by the teenager's ability, even after playing alongside some of the game's most gifted footballers.
"Before I left Barcelona, I told Lamine Yamal that I had played with some very talented players, but he is above all of them," Rashford said.
"I've never seen a player of that age with so much talent. He is the closest anyone can get to the level of Messi over the years."
Yamal has already established himself among the leading players in world football, finishing second, third and eighth in the Ballon d'Or voting at the age of 19. Rashford believes those achievements are only the beginning.
"I believe so much in this boy's talent. If he goes on to win seven Ballon d'Or awards, I wouldn't be surprised. He's finished second, third and eighth. And at what age? 19?"
Rashford was careful to distinguish his admiration for Yamal from the extraordinary status of Messi, whom he believes remains in a category of his own.
"He's an incredible player. We'll probably never see another player in our lifetime in terms of a complete genius like Leo."
The forward also discussed the Ballon d'Or awarded to Harry Kane, believing the striker's goals and assists made him a deserving winner.
"He scored a ridiculous number of goals this year and a ridiculous number of assists. I sent him a text the other day and told him he deserved it."
Rashford was also asked about his decision to move abroad rather than join another Premier League club after leaving Manchester United.
"I couldn't keep playing against United every season. If United wasn't an option, I told my agent to take me abroad. Don't take me to another Premier League club."