Beckham suffered a setback when proposals to build a new 25,000-capacity stadium were rejected in 2014.
One of Beckham's partners, Sprint chief executive Marcelo Claure, said the group had "presented our intentions" to Miami mayor Tomas Regalado.
Ex-England captain Beckham played for MLS side LA Galaxy from 2007 to 2012.
In February 2014 he announced he was starting a new Miami-based franchise to play in the MLS.
But plans to build a new stadium on a city waterfront next to a basketball arena were rejected.
In February, Beckham remained confident of his project succeeding. He said: "Delays are frustrating but we will get it right and it will happen."