The pair crossed paths at a recent ceremony to crown the UEFA Men's Player of the Year for 2018-19, which Liverpool defender Virgil van Dijk won.
Barcelona captain Messi and Juventus star Ronaldo finished second and third respectively, but the event gave the former Real Madrid forward the chance to publicly reflect on their "battle in Spain" and the time they have spent at the pinnacle of the game.
Ronaldo floated the prospect of a private dinner in future, an idea welcomed by his fellow five-time Ballon d'Or winner.
"Yes, I don't have any problem with that," Messi told SPORT.
"I've always said that I don't have any issue with him. We might not be friends because we've never shared a dressing room together, but I always see him at award shows and there's no problem.
"We actually spoke with each other for quite a long time at the most recent show.
"I don't know if there will be a dinner because I don't know if our paths will cross for obvious reasons, each one of us has our own life and our own commitments. But obviously I would accept the invitation."