The 25-year-old former Newcastle defender has played for his country at youth level but awaits his big break with the World Cup-winning senior squad.
Enrique has been performing consistently for the Reds since his summer move from the Magpies and is hoping to catch the eye of national team boss Vicente del Bosque.
Asked of his potential involvement with Spain, he told Liverpool's official website: "I think if I keep improving I can be there.
"I haven't gone yet because it's really hard to go - we won the last World Cup and the last European Championships, but I hope in the future I can be there."
Del Bosque is soon due to name his squad for Spain's upcoming fixtures with
Czech Republic and Scotland next month, but Enrique faces competition from former Liverpool defender Alvaro Arbeloa and Atletico Madrid's Alvaro Dominguez.
He added: "When I signed here I wanted to play Champions League football with this club and also to try and go to the national team.
"If I go I'll be happy but for me the national team is an extra. It's important but for me it's my club first."
And for his club Enrique has earned rave reviews from Liverpool fans, who has so often bemoaned their lack of defensive quality in the left-back position.
The Spaniard, though, is taking little for granted: "To get the fans with you, you have to play well. At the moment I think I've done well but I can do better.
"I have to improve of course. Sometimes I think about my mistakes and I want to kick myself.
"I'm like every person - I know when I've done good things and I know when I've done bad things. In football it's the same. I always think about my mistakes."