Inter Miami co-owner Beckham was speaking at a fan event at the weekend ahead of the MLS pre-season.
Beckham was asked by reporters if he had an interest in signing either Ronaldo or Messi to his team, to which he responded: “Without a doubt, those are the type of players that we aspire to bring to our club.
He added: “I think that the fans would really appreciate that. But, you know, as owners, we want players here that are driven, that want to win, and that’s our priority.
“With [current players] Blaise Matuidi and Gonzalo (Higuain), 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 (Messi) and Cristiano (Ronaldo).
“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.”