Beckham co-owns the new Major League Soccer franchise who made their debut in the United States top flight last season and finished 10th in the Eastern Conference.
Inter Miami have already added French world cup winner Blaise Matuidi and former Real Madrid, Juventus, Napoli and Chelsea striker Gonzalo Higuain to their ranks while Phil Neville has left his role as England women’s manager to become the club’s new head coach.
Messi, whose contract with Barcelona expires this summer, has expressed interest in playing in the MLS in future and Ronaldo’s contract with Juventus runs out next summer.
Beckham, speaking at a fan event ahead of the 2021 MLS pre-season, said when quizzed on interest in Messi and Ronaldo: “Without a doubt, those are the type of players that we aspire to bring to our club.
“I think that the fans would really appreciate that. But, as owners, we want players here that are driven, that want to win, and that's our priority.
“With Blaise Matuidi and Gonzalo, these are players that we feel add to the glitz and the glamour of what the club is.
“Going forward, we also want to bring other players in if we have the opportunity to bring some great names in, you obviously mentioned Leo and Cristiano.
“They've been at the top of their game for the last 15 years because of hard work. Sir Alex Ferguson was a master at it.
“He didn't always bring in the best player in the world. He didn't always bring in the top player. He bought the right player for the club. And I think that that's the one thing that I take into our club, is the player has to be right.”
