Cruise operators have raised concerns about traffic problems if the 25,000-seater stadium for the Major League Soccer franchise in the heart of Port Miami receives the go-ahead.
Beckham attended a news conference in Miami on Monday to announce the development plans and said of the opposition: "I want to change their minds.
"I don't want to be an enemy to the people that are opposed to the stadium. I want to work with them."
Beckham has also hired a lobbyist to try to secure state aid from Florida to part-fund the stadium, according to the Miami Herald. Other stadiums in the state receive annual aid.
Beckham added: "We want to be treated like every other franchise. We're not asking for anything more or anything less."