An MLS source told The Sun: "Becks understands the need for a big, big name in the team when it gets going.
"And none come bigger than Ronaldo - the world's greatest player. Ronaldo loves America and all that it offers.
"It's not a secret he has thought about finishing his career here, about living here - so a deal like this could be perfect for him."
The source claimed that any potential deal would be in 2017 - at the earliest - but that the possibility of signing such a global icon showed Beckham's ambition for his franchise.