The La Liga side took the unusual step of publicising the fact that Llorente had refused to attend a media event after training in the morning, stirring up further speculation over the 27-year-old's future at the club.
"They told me just as I was leaving training and I didn't have time," Llorente told local television station Telebilbao, to whom he said he had already agreed to speak.
"I can't be in two places at once. I don't have a problem with speaking on another day."
Bilbao had said on their official Twitter feed ahead of a news conference with defender Jon Aurtenetxe: "No other player will be speaking after the refusal of Fernando Llorente to appear in front of the media."
They repeated the message afterwards as well.
Llorente, known as the 'Lion King', turned down a contract extension beyond 2013 in the close season but Bilbao have refused to negotiate with interested parties.
Coach Marcelo Bielsa has since relegated Bilbao's top scorer last season, when they reached the final of the Europa League and Copa del Rey, to the bench and Llorente has yet to start a La Liga match this term.
Llorente's former club team-mate Javi Martinez, who forced his own Bilbao exit to Bayern Munich in August by travelling to Germany without the club's permission before being bought out of his contract for 40 million euros, sympathised.
"I know he has been going through some tough times," Martinez said in Valencia ahead of Bayern's Champions League Group F clash at the Mestalla.
"All I can do from here is wish him well and hope that everything is sorted out for him soon," he said of his Spain team mate, who has scored once in 14 appearances this season in all competitions.
Last week, Bilbao president Josu Urrutia indicated the club had no intention of letting Llorente go in the January transfer window, adding that there did not appear to have been any change of heart from the player to stay.
Llorente, who has a buy-out clause of 36 million euros, said he was trying to put on a brave face.
"I have told the club I didn't like the way they were treating me. The stories in the media have been really bad and haven't helped the situation at all. Things have become twisted," he said.
"I am not doing anything bad. I am trying be good. I have suffered inside but I try to show externally I am ok."