Beckham was speaking at a fan event on the weekend, alongside the MLS club's managing owner, Jorge Mas, ahead of the first team's preseason.
Asked whether he has interest in signing the Barcelona or Juventus stars, two players who have shown some interest in playing in MLS as their careers wind down, Beckham said "Without a doubt, those are the type of players that we aspire to bring to our club."
Ronaldo is understood to be interested by the challenge of joining the club in the United States.
The financial contract would be massive for Ronaldo but he may potentially make the move next January, lowering the transfer fee, given the MLS runs from March to December.
Messi was reportedly previously sounded out about a possible US switch.