In an interview with the Miami Herald published Tuesday, Inter Miami Jorge Mas said Messi was likely to play his first game for Inter on July 21 against Mexican side Cruz Azul in the regional Leagues Cup competition.
Argentina captain Messi confirmed on June 7 that he plans to head to U.S. "Major League Soccer" after ending a two-year stint with Paris Saint-Germain.
The deal has yet to be finalized, but the Herald, citing a source with knowledge of the negotiations, said Messi was joining on a two-and-a-half-year deal worth up to $60 million a year.
The deal also included an equity stake in Miami "upon the end of his playing days," the Herald report said.
Mas, meanwhile, told the paper that Messi's contract would conform to MLS roster rules.
"There are no categories or anything that is being changed to incorporate Lionel Messi onto Inter Miami's roster," he said.
Mas said Messi's arrival in MLS would prove to be a "seminal moment" for the history of football in the United States.
"I think there will always be a before and after Messi when we talk about the sport in the United States," Mas said.
"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."
Miami, meanwhile, are widely reported to be in talks to bring Messi's former Barcelona teammate Sergio Busquets to Florida. Mas would not comment on the state of negotiations with Busquets, and would not name other players - such as Jordi Alba, Luis Suarez and Angel di Maria - who have all been linked to Miami.
However, Mas said the club expected to make between three to five additional signings.
"We've been preparing our roster for Messi's arrival in '23, so we left an enormous amount of flexibility," Mas told the Herald.
"We will be making additional signings during the summer window, more than what people anticipate... I can say we will potentially be making between three and five signings."