The 21-year-old midfielder is considered to be one of the most exciting talents in European football, but he faces fierce competition for places at Santiago Bernabeu.
He has benefitted from the enforced absence of others this season to make 24 appearances in all competitions, but the return to fitness of Gareth Bale et al could see his game time limited over the second half of the campaign.
He told Club del Deportista on his future plans: “It is difficult to manage a squad as good as our one, but [Zinedine] Zidane knows he can count on me.
“I work hard every day to earn more minutes, but I am aware of where I am.
“I am at the best club in the world and I am happy at Real Madrid.”
Asensio proved his worth to Real over the course of the 2016-17 campaign, as he made a career-best 38 appearances and netted 10 goals.
He has already added another seven efforts to that tally this term, but is by no means assured of a regular place in Zidane’s plans.
The youngster needs game time, though, if he is to maintain his impressive development while pushing for a place in Spain’s squad for next summer’s World Cup.