Such a move would provide a huge boost to the sport in North America ahead of the World Cup in 2026, which will be held in the USA, Canada and Mexico, with Messi previously indicating a desire to play in MLS.
However, his representative Marcelo Mendez has dubbed the reports as "fake news" and made it clear discussions are not taking place.
"It's false, it's fake news. There is no negotiation for Lionel to join Inter Miami next season," Mendez said.
Messi is currently focused on leading Argentina to glory in the World Cup, having scored in both of his side's matches so far – including the opening goal in the crucial victory over Mexico on Saturday.
Argentina meets Poland on Thursday (AED)T, where victory will secure a spot in the knockout stage. A draw would also be enough if Saudi Arabia and Mexico finishes level in the other Group C match.