Llorente was the top Spanish scorer in the Primera Division last season, but he has fallen out with the Athletic hierarchy this term and has decided to leave when his contract expires in June.
Tottenham, Manchester City and Arsenal have all been linked with the 27-year-old Spain international and he admits a move to England interests him.
"I really like the Premier League and I've mentioned on more than one occasion that it's a league which appeals to me a lot," Llorente told Sky Sports.
"You never know. It's one good option in terms of my future but we'll have to wait until the end of the season to see what happens.
"It is true that we are approaching the date when I can sign for other clubs.
"I'm trying to keep it so that it is something which is managed by my brother and my representatives. That leaves me to focus on my football and help my team, Athletic, and nothing else, maintain focus."
Reports had claimed Llorente had already agreed a deal to sign for Serie A leaders Juventus, but he insists that is not the case.
"No. That's totally untrue," Llorente said.
"I think it's normal that people talk about these things, but ultimately you have to respect the rules.
"I am an Athletic player and, until January 1, I cannot sign with any other team."
Llorente has fallen out of favour with manager Marcelo Bielsa since turning down a new contract in the summer. The striker, who was part of Spain's recent World Cup and Euro 2012 winning squads, has only started one Primera Division game this season.
He feels he has been pushed out of the club by pressure from the media and the Athletic supporters.
"I made the decision at the start of the season," Llorente said.
"We were playing a Europa League qualification game at San Mames and I noticed a significant deterioration in the relationship between the fans and me due to my protracted contract negotiations.
"Everything the press had written about me in the newspapers was pejorative and they succeeded in turning the fans against me.
"It was when I became fully aware of how that situation had affected the supporters that I made the decision.
"Ultimately you have to bear the situation for a long time and you get tired of living like that."