The conclusion of the revamped, expanded Club World Cup - which included extensive pre-match entertainment and a half-time show - was attended by 81,118 people at MetLife Stadium.
Trump watched Chelsea's impressive victory in the final alongside Infantino and said in an interview with Dazn at half-time that he was "having a really great time".
In a longer interview broadcast later on Sunday, he added: "Gianni is a friend of mine, he's done such a great job with the league and with soccer - or as they would call it 'football', but I guess we call it soccer. I'm not sure that change could be made very easily.
"But it's great to watch - and this is a little bit of an upset that we're watching today, isn't it?"
When it was suggested he could make an executive order so that the sport was referred to as "football" from now on, Trump smiled and said: "I think we could do that. I think I could do that."
The United States, along with Canada and Mexico, will jointly host the 2026 men's World Cup next summer.
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