The 37-year-old, who has been with Liverpool for the past five seasons, wants a short stint in his homeland before he retires.
I would like to return to La Liga after 11 seasons in the Premier League," said Adrian to Mucho Deporte.
"It would be the end of a cycle. I'm still ready to compete. I feel very good despite being 37.
You know that goalkeepers, if you take good care of yourself, if you haven't had any serious injuries lately and you're fine, the daily training gives you that intensity that makes you compete.
I think Adrian has a long time left and it's true that I would like to return to La Liga. It has to be a nice, interesting project."
Adrian added: I haven't sat down with Liverpool yet either. I don't rule out that we could have a pending conversation, but it is true that we will be looking out of the corner of our eye to see what happens in La Liga."