Totally understandable how annoying this can be. I have a colleague like this (incidentally from the USA). He isn’t even in the same office with me - I can hear him through the wall, and I don’t know how people stay in the same room with him 8 hours a day. He won’t shut the fuck up. But realistically speaking, just weigh your options: how annoying is he and how much do you care about potential animosity.

Whether you talk to the manager or to him, he will most likely take it personally. I doubt the manager will do anything, but it will agitate the guy. Same if you make your point explicitly clear to him - he will not like what you say, and therefore you. If you can live with it, go ahead. I’ve done it multiple times, and honestly, it felt pretty awesome. There was a lot of drama, and afterwards, they started talking shit about me to other colleagues and managers, but I couldn’t care less. Good times. Not everyone is like me though, so it’s entirely your decision. Either way, it sucks.