Asensio started the 2017-2018 season strongly, scoring in both legs of the Supercopa de Espana triumph over Barcelona, but struggled to retain a place in Zinedine Zidane's star-studded side.
The 22 year-old signed a six-year contract, which reportedly includes a €700million buyout clause, at the Santiago Bernabeu last September, but has been linked with an off-season switch to Anfield.
Asensio came off the bench in Spain's World Cup win over Iran and the 2-2 draw against Morocco - a result that sent it through to the last 16 as Group B winner - and says the national team is his sole focus for the time being.
Asked about Liverpool's interest, Asensio said: "That's something in the news but I'm very focused in the World Cup.
"When it ends, we can talk about that kind of thing. I'm very focused here in Russia, on the national team and performing well here."
David de Gea has come under intense scrutiny after an error gave Cristiano Ronaldo his second goal in their opening draw, while he has conceded five goals from six shots on targets.
However, Asensio is confident the Manchester United goalkeeper will prove why he is widely considered to be one of the best in his position.
"I see him calm. He couldn't do much more on the goals [against Morocco]," Asensio said. "The national team keeper is a very demanding role, but he is more than prepared.
"He is willing and he is calm and I'm sure we'll see the sort of performances he has previously shown for the remainder of this World Cup."
Spain's campaign was thrown into turmoil when they sacked Julen Lopetegui just two days before their opening match, the coach having agreed to join Madrid less than 24 hours beforehand.
Fernando Hierro was installed as his replacement for the competition, and Asensio thinks the adversity has brought greater cohesion to the squad.
"We went through a weird situation that nobody expected and that could have affected us a bit. But we talked it through, we had to remain united, a World Cup is only every four years and is very important for us," added Asensio.
"Every game is a new challenge, it is very difficult to beat any team and that is what we are seeing."