He would go on to be included in the Best XI team of the tournament. On 7 July 2016, Montes was named in Mexico's 21-man squad that would participate in the 2016 Summer Olympics in Rio de Janeiro, Brazil. He would appear in all of Mexico's group stage matches but Mexico would finish third in their group and were thus eliminated from the competition. He was called up by the senior national team to participate in the 2017 CONCACAF Gold Cup. He would make his debut on 13 July 2017 during a group stage match against Jamaica, coming in as a substitute for Rodolfo Pizarro at half-time, finishing the game at 0–0. On 6 June 2019, Montes was called up by coach Gerardo Martino to participate in the CONCACAF Gold Cup. He appeared as a substitute in the group stage match against Cuba and as a starter in the final group stage match against Martinique as Mexico went on to win the tournament. A ball-playing defender that has shown maturity despite at a young age, Montes has a great range of passing, and has shown on a few occasions that he’s able to pick out long-range passes, can execute a well-timed, and accurate, slide tackle, has shown he is capable of contributing goals in set-pieces, and is good in the air and able to deal with high balls into the box.