Born in Palma, Majorca, Balearic Islands to a Dutch mother and a Spanish father, Asensio played youth football for hometown club RCD Mallorca. After being scouted by Real Madrid and FC Barcelona, he made his senior debuts with the B-team in the 2013–14 season in Tercera División, despite still being a junior; on 27 October 2013, he made his first competitive appearance for the main squad, playing the last six minutes in a 1–3 away loss against Recreativo de Huelva for the Segunda División championship.
Again from the bench, Asensio played the last six minutes in a 0–0 home draw against CD Lugo. After impressing in his first games, he was promoted to the first team by manager José Luis Oltra.
Asensio scored his first professional goal on 16 March 2014, netting the first in a 2–0 home win over CD Tenerife. He was made a starter under new coach Valeri Karpin, scoring against CA Osasuna, Deportivo Alavés and UE Llagostera within a month.
On 24 November 2014, Real Madrid reached an agreement in principle to sign Asensio. On 5 December the deal was officially announced, with the player signing a six-year deal for a €3.9 million fee and remaining with the Bermellones on loan until the end of the campaign.
On 20 August 2015, after making the whole pre-season with Real Madrid, Asensio was loaned to RCD Espanyol in La Liga. He played his first game in the competition on 19 September, featuring 86 minutes in a 3–2 success at Real Sociedad, and he ended his spell at the Estadi Cornellà-El Prat with 12 overall assists.
Returned to the Santiago Bernabéu Stadium for 2016–17, Asensio’s first competitive appearance took place on 9 August, as he played the full 120 minutes and scored through a 25-meter effort in a 3–2 win against fellow Spaniards Sevilla FC for the UEFA Super Cup. He made his first league start 12 days later, netting the second goal in a 3–0 success at Real Sociedad.
After being a regular for Spain at youth level, Asensio made his debut for the under-21 team on 26 March 2015, coming on as a late substitute for goalscorer Gerard Deulofeu in a 2–0 friendly win over Norway in Cartagena. In July, he was part of the victorious under-19 team at the UEFA European Championship in Greece, where he scored both goals in a semi-final victory over France in Katerini, in the 88th minute and in added time.
On 17 May 2016, Asensio and Espanyol teammate Pau López were called up to the full side for a friendly against Bosnia and Herzegovina.He made his debut on the 29th, starting in the 3–1 win in Switzerland.
ClubSeasonLeagueCup1ContinentalTotalDivisionAppsGoalsAppsGoalsAppsGoalsAppsGoalsMallorca B2013–14Tercera División143—143Mallorca2013–14Segunda División20100—2012014–1536600—366Total56700—567Espanyol2015–16La Liga34430—374Real Madrid2016–17La Liga1224331196Career total11616733112620