The 35-year-old joined the Major League Soccer outfit after leaving Paris Saint-Germain as a free agent at the end of the season.
Inter Miami face Mexico's Cruz Azul in a domestic cup clash on June 21 at DRV PNK Stadium in Fort Lauderdale, Florida.
According to The Miami Herald, Messi could be made available for the match.
Inter Miami owner Jorge Mas has revealed a deal is in place for Messi, but they are still finalising the agreement.
The club will move to a new stadium in 2025, but improvements will be made to the DRV PNK Stadium in order to help with demand.
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"We have already contracted to fill in the corners of the stadium that should increase capacity by approximately 3,000 to 3,200 seats [to a capacity of around 22,000]," he said.
"We are gearing up to do that work in the next four weeks. Every game will be sold out. The demand for tickets has been 10 times what we can handle on a season ticket basis."
The Argentine has had one of the most successful careers in football, winning near enough every big trophy on offer - including the World Cup in December.
Messi finally lifted the trophy in Qatar when Argentina beat France in a pulsating 3-3 final in Doha that the Albiceleste won on penalties.
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It adds to an already hefty trophy cabinet that contains LaLiga, Ligue 1 and Champions League titles.
And that also includes seven Ballon d'Or accolades - while he is the favourite to go on and win an eighth this year.
And that also includes seven Ballon d'Or accolades - while he is the favourite to go on and win an eighth this year.
Inter Miami chief Mas, previously said Messi arrival is a 'the one seminal moment' in the history of US football.
"I think there will always be a before and after Messi when we talk about the sport in the United States.
"I have a very, very strong held belief that we can create in North America and the United States if not the greatest league, one of the top two leagues in the world."
"I cannot over emphasize the magnitude of this announcement. Having the world's greatest player here is something that is significant for our league, and for the football ecosystem in the United States.
"Lionel Messi is coming to this country to win cups and make a difference. I think it's incumbent upon myself and my partners in the league, the other owners, to seize the moment."