Four-time world champions Italy failed to qualify for Russia 2018, Qatar 2022 and now North America 2026, the first edition to feature 48 teams.
"We have had discussions about expanding to 64 teams... the matter was presented to the FIFA council," Infantino told Brazilian digital broadcaster CazeTV on Thursday before the World Cup opener, which Mexico won 2-0 against South Africa.
"Maybe Italy qualify with 64 teams, or we could even go up to 208 teams," he added with a laugh in a brief interview as he entered Mexico City's Azteca Stadium.
South American Football Confederation (CONMEBOL) president Alejandro Dominguez of Paraguay is promoting a proposal to expand the 2030 World Cup to 64 teams to mark the centenary of the tournament's first edition, Uruguay 1930.
Part of the event will be held in Paraguay, Uruguay and Argentina as a nod to the tournament's history, but the main host nations will be Spain, Portugal and Morocco.
"We first have to see how this first World Cup with 48 teams goes," Infantino said.
Italy's sports minister Andrea Abodi was widely quoted by media as saying that he wanted to speak to Infantino as he was left "perplexed" by his comments.
"Given that there is a big distance between Italy and Mexico, I'd rather speak to him on the telephone to understand (what he meant)," said Abodi.
"I'd like to hear from him directly."