It is an international sport. However, given the need to train with elite coaches and training partners, many international fighters do some of their training in the US once they reach the highest levels of the sport.
All of the current UFC champions have done significant training in the US. Some even live in the US. Francis Ngannou has been living in Las Vegas for over 3 years now. Valentina Shevchenko lives there as well. Amanda Nunes has been living in Florida for many years. Kamaru Usman moved to the US as a child and has lived there for over 25 years.
Early in his career, Jan Blachowicz spent a lot of time training in San Diego because UFC fighter Tomasz Drwal lived there.
Israel Adesanya has spent several months at a time trying to shore up his ground game by training with Andre Galvão at Atos in San Diego.
Charles Oliveira spent nearly a decade fighting out of Houston, because he trained there with Macaco Gold Team in addition to training with Chute Boxe Diego Lima in São Paulo.
Alexander Volkanovski hadn't trained much in the US, prior to coaching TUF, but his long-time wrestling coach, Frank Hickman, is a D1 wrestler from North Carolina. Hickman also works with Israel Adesanya to improve his TDD.
Deiveson Figueiredo spent two years training at Team Alpha Male in Sacramento.