The 36-year-old Inter Miami forward is currently preparing for Argentina's Copa America title defence, which runs from June 20th to July 14th in the United States.
In February, under-23 manager Javier Mascherano said Messi, who won gold with Argentina at the 2008 Beijing Olympics, had an invitation to join the squad for Paris.
"I talked to Mascherano and the truth is we both understood the situation," Messi told ESPN.
"It's hard (to think about the Olympics right now) because we're in Copa America. It would be two, three straight months of not being with the club, and more than anything I'm not at an age to be in everything.
"I have to choose carefully, and it would be too much to play two straight tournaments. I've been very lucky to play in the Olympics, of winning it together with (Mascherano).
"It was a wonderful experience on a football level. Olympics, U20, memories I'll never forget."
The men's football tournament at the Olympics takes place in July and August. Teams are allowed three over-age players in their squads.