The mayor of Miami Dade, Carlos Gimenez, said negotiations for the stadium started last week.
"There's going to be a few bumps along the way, but we're going to make the team in Miami not just the best team in America, we're going to take the team global," Beckham told a reception for city leaders at Miami's performing arts centre on Tuesday night.
The former Manchester United and Real Madrid star, who also played for the Los Angeles Galaxy, retired as a player last May and holds a $25 million option in his MLS contract to start a new franchise.
Beckham is already in discussions with Miami-Dade County about leasing county-owned land for a 25,000-seat stadium.
"I have seen the atmosphere around the city," Beckham told the media Tuesday outside the reception, referring to scenes last year when the city's basketball team, the Miami Heat, captured the National Basketball Association (NBA) championship.
"I saw the passion of the people for sport," he said.
Beckham, 38, arrived in Miami fresh from having attended Sunday's Superbowl in New Jersey, TV coverage of which featured a fit Beckham in an underwear commercial.
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Beckham's investment group has narrowed its stadium search to five possible sites in and around downtown Miami, officials say, including a 25-acre (10-hectare) waterfront lot next to the port of Miami's cruise ship terminals, potentially putting the new team at the forefront of Miami's tourism landscape.
MLS has stressed the importance of having a final stadium deal, along with a business plan, before it will approve a new team.
Beckham's group is not looking for public financing, but may need to negotiate site plans with the county, such as leasing the port location, to help build a privately financed stadium.
Beckham has toured Miami twice in recent months with British businessman and American Idol creator Simon Fuller, as well as Bolivian-born billionaire Marcelo Claure, founder of Miami-based Brightstar Corp., the world's largest wireless distributor and the provider of global services to Apple.
Beckham is also looking for a pad in Miami, although the London house he shares with his wife of 14 years, former pop star-turned-fashion designer Victoria Beckham, and their four young children, will remain the main family home.
"We are going to be spending a lot of time here," he told the media on Tuesday. "We are hoping to get our own place here as well."