Beckham, who had the option to purchase a franchise included in his contract with the MLS when he signed for Los Angeles Galaxy back in 2007, announced his intention to take a team to the Floridian city late last month.
James already has a stake in Premier League side Liverpool, and revealed he is keen to help the former England international with his ambitions.
"There's some interest in both sides," James said in quotes reported by ESPN.
"David has become a good friend of mine over the last few years, and I think it would be great for this city to have a football club for sure.
Two-time NBA champion James admitted discussions are still at a preliminary stage, but is confident that the project can be a success.
"The research is still being made out, but I think it can be huge," he added.
"I think this is a great town for soccer. There are a lot of soccer players here. There is a lot of great youth soccer here."
Miami's last MLS franchise folded in 2002, when Miami Fusion were withdrawn from the league after just four seasons.
