Born in Dos Torres, Province of Córdoba, Medrán joined Real Madrid's youth setup in 2011, aged 17.

After being promoted to the C team the following year he played his first match as a senior on 23 February 2014, coming on as a second-half substitute in a 2–0 away win against Real Zaragoza for the reserves in the Segunda División.

[4] Medrán made his first-team – and La Liga – debut on 18 October 2014, replacing Luka Modrić in the 79th minute of a 5–0 away rout of Levante UD.

[13] After the appointment of new manager Abelardo Fernández in December, however, he was rarely played,[14] which led to the player bursting into tears in a post-match interview following a league fixture at UD Las Palmas in April 2018 where he featured 16 minutes and netted once (4–0).

[16][17] On 10 October 2019, Medrán was announced as a new signing by Major League Soccer side Chicago Fire FC ahead of the upcoming season.