The striker will not renew his contract with Marcelo Bielsa's team and will be available on a free transfer in June, but claims his decision was not affected by the press or fans.
The Spain international has been linked with a move away from San Mames throughout 2012 after falling out with coach Marcelo Bielsa, with Juventus among the clubs that have been rumored to be interested in the forward.
The 27-year-old is out of contract in June, and when he was questioned at a press conference as to whether he would be departing Los Leones in the summer, he said: "Yes. It's not about the money and I have not felt blackmailed by the club.
"Looking back at what has happened since I made my first appearance at San Mames has made this a sad decision."
Llorente claimed that the press has not made the situation any easier for him due to the number of rumors about his future that have been circulating in the media, though he claimed that was not the reason for his decision.
He also thanked the club's fans and players for their support.
"The press has not helped anything. They have successfully increased the bad environment, but leaving the team is for other reasons," he said. "I feel loved by the fans. The players are with me and I really appreciate it."
Despite explaining his desire to leave, the striker has reiterated that he wants to contribute for the remainder of the season, starting with the club's Europa League game against Sparta Prague on Thursday.
"I want to play. The atmosphere will be fantastic, but we must also play our part."