Asensio has scored 21 times in 95 appearances for Madrid since his arrival from Mallorca, including 11 goals in 53 matches for the European champions last term.
The 22-year-old was linked with a move to the Premier League during the summer transfer window, with the likes of Liverpool and Manchester United said to be interested in the attacker.
Asensio, however, has said that he never thought about leaving Los Blancos following the departure of Zinedine Zidane as head coach.
"I've never had the intention to go anywhere," Asensio told reporters.
Asensio scored once and provided four assists as Spain thumped Croatia 6-0 in the UEFA Nations League on Tuesday night.