The Athletic trainer says that he would love the powerful striker to stay at the club and denies claims that their approach to contract negotiations could be classed as blackmail
The Liga side have been accused of blackmailing the 27-year-old by players' union FIFPro because they were refusing to play him until he signed a new contract.
But the Argentine boss insists the club are doing everything above board.
"What we are doing is perfectly legitimate and sincere, we are not blackmailing the player," Bielsa told Terra.
Llorente's contract is up at the end of this season and has been linked with a move to Juventus, but his current coach says he wants the striker to commit his long-term future to the Basque outfit.
He added: "I would be pleased if we could arrange a new deal with Llorente. I want him to remain with Athletic Bilbao for the rest of his career."
Llorente has made eight appearances in La Liga this term finding the net once.