Barcelona captain Messi and Juventus forward Ronaldo have both been linked with moves to the United States – Beckham's expansion franchise Inter looming as a possible destination for the pair.
There is speculation Inter, who will make their MLS debut against Los Angeles FC on Sunday, could lure both players to Miami after Minnesota United head coach Adrian Heath talked up the possibility.
Inter co-owner Beckham addressed the speculation during his appearance on 'The Tonight Show Starring Jimmy Fallon' on Wednesday.
"Well you know what, we've got great opportunities down in Miami," former Manchester United, Real Madrid and England star Beckham said with a smile.
"We've been contacted by a lot of different players with possibly coming to join the team. As any owner, you really want the best players and if we have the opportunity to bring in players like Cristiano or Leo, I have such admiration for them as athletes, if we could bring those players in than great.
"But at the moment, we have a great roster. Young players, a couple of experienced players too, but a lot of young players who are just ready to play.
"One of the things I learnt from [former United manager] Alex Ferguson… he turned around to me and said whoever you bring in, they have to be the right fit for the club. It's not about the biggest name or personality, it's about who fits in best with the players.
"That's what we'll do. But like I said, as an owner if you want to bring these players in than we have a great opportunity."
Inter, who have also been linked to Manchester City's David Silva, Paris Saint-Germain forward Edinson Cavani and Real Madrid midfielder Luka Modric, have a Designated Player spot available after signing Rodolfo Pizarro and Matias Pellegrini.