During a youth league playoff match with Pob. Miguel Alemán against Monterrey, he caught the attention of the opposing team. He was eventually brought onto Monterrey's youth team and on 2 August 2015, Montes played his first match with Monterrey against Portuguese team Benfica on the inauguration of the Estadio BBVA Bancomer. Montes came in as a substitute for the second half, and at the 48th minute he scored the first ever-goal in the Estadio BBVA Bancomer. Monterrey defeated Benfica 3–0. Montes made his official debut for Monterrey on 29 July 2015, against Correcaminos UAT in an Apertura 2015 Copa MXgroup stage match, where Monterrey defeated Correcaminos 3–1. At the end of the 2016 Clausura, he was listed in the Bext XI. At the end of December 2019, he would win the 2019 Apertura finals against América. Clásico Regiomontano Clásico Regiomontano matches against crosstown rivals Tigres UANL have proven to be significant for Montes, scoring three goals against them to date. He would make his league debut on 19 September 2015 against Tigres UANL, contributing a 40-meter long ball assist to Rogelio Funes Mori to score the only goal for Monterrey where they lost Monterrey lost 3–1. On 14 May 2016, he would score Monterrey's only goal of the second leg of the Clausura 2016 championship quarter-final against Tigres UANL, losing 2–1, but with an aggregate score of 4–3 in favor of Monterrey to allow them move onto the semi-final against América. On 29 October 2016, he would tie the game against Tigres UANL, 1–1. On 21 April 2017, Montes scored the only goal in a 1–0 victory over Tigres UANL.
International career
Mexico U-21
He was part of the roster that participated in the 2018 Toulon Tournament. He would go on to appear in all group stage matches including the semi-final, except for the final where Mexico would go to lose 1–2 against England since he picked up an injury in the previous match against Turkey. He would go on to be included in the Best XI team of the tournament.
Mexico U-23
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.
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.