[5] He was highly recommended by Real Madrid legend Zinedine Zidane to take into their youth system and was viewed as 'the next Falcao' due to his goalscoring abilities.
[6] Narváez made his debut for the club in the 2013 Copa del Rey Juvenil, where he scored two goals in three appearances as the team won the trophy, although he did not play in the final.
He made his first team debut on 28 January 2012, playing the whole game in a 3–0 win over Zamalek SC in the Alkass International Cup.
Narváez made his UEFA Youth League debut against Galatasaray, as he managed to score the tying goal in a 1–1 draw.
[15] On 29 January 2018, Narváez he was loaned to Segunda División side Córdoba CF,[17] where he helped to avoid relegation in the last game of the season by winning 3–0 to Sporting Gijón.
[19] Upon returning, he was initially assigned to Betis' first team in La Liga, but moved to Las Palmas still in the second division on loan for one year on 31 August 2019.
[27] Narváez was repeatedly called up to participate in Colombia's U20 squad, but Real Madrid refused to release him; he was not allowed to take part in the 2015 FIFA U-20 World Cup.