The Florida side have been linked with every big name in the sport, but it is now believed they would go out to make the biggest statement possible and sign the Argentine.
Messi's contract with Barcelona runs until 2021, but he would be 33 by the time Miami play their first game and a huge bid could be enough for both the player and Barcelona to be convinced.
According to the 'Daily Mail', sources close to Beckham insist that no contact has been made, but that Messi would be the prime target if he could be tempted to leave Catalonia.
One plus for the MLS side is that Messi's favoured option of a return to Argentina has grown less likely, due to his problems and percieved failings with the national side.
In addition, Miami - where the population is 70% Latino - would be the perfect option for Spanish-speaking Messi, and it is withoud doubt the area of the USA where he is most popular.