Born in Berwyn, Illinois, to Mexican parents, Gutiérrez grew up within the U.S. soccer system and even featured for the U.S. youth national teams. Gutiérrez made his senior national team debut for the USMNT in January 2025 during an international friendly camp and earned his first two caps in matches against Venezuela and Costa Rica. He was later called up to the roster for the CONCACAF Nations League Finals in March 2025.
However, because those games were not official competitions, the 22-year-old remains eligible to switch federations and represent Mexico at the international level.