The former England captain who retired earlier this year after stints with Manchester United, Real Madrid and the MLS club L.A. Galaxy, had been considering several locations and toured Miami this summer, meeting with city and county leaders.
His MLS player contract included an option to create a new team for $25 million.
Beckham was still putting together a team of investors, the source said. The person spoke on condition of anonymity because Beckham's plans have yet to be officially announced.
His representatives are already looking at sites for a purpose-built soccer-only stadium, according to a well-placed source in Miami's business community.
"They have people looking real hard. They want to be in the urban core," the person said.
A fan group which has been campaigning for a team to come to the city welcomed the news. Julio Caballero, spokesman for the group, which calls itself MLS Miami Bid, posted "It's our time," on the group's Facebook page.
MLS confirmed it was in discussions with Beckham but declined to confirm if a deal had been struck.
"We are continuing our discussions with David Beckham regarding future ownership of an MLS expansion team," said Dan Courtemanche, a spokesman for MLS.
"Our policy regarding discussions with potential expansion team owners is that we keep those conversations private until the individuals we are speaking with decide they want to go public with their plans. Thus, it is more appropriate for David Beckham to comment on his plans."
Miami officials also reacted cautiously to the news. "We've not had any official notification that David Beckham has chosen Miami for a new Major League Soccer (MLS) franchise," Miami-Dade County Mayor Carlos Gimenez said in a statement.
"That said, I join the hundreds of thousands of soccer fans throughout South Florida who are ready and eagerly waiting for an MLS team to be established in Miami. A world-class community like Miami-Dade County, also known as the Gateway to the Americas, would be a fitting home for the world's most popular sport."
The greater Miami area has a large and growing Latin American population and local sports bars always draw large crowds during the World Cup soccer tournament every four years.
More than 70,000 fans attended an International Champions Cup match in Miami between Real Madrid and Chelsea in August.