The 27-year-old's contract is up at San Mames at the end of the season and the Spanish internationalist said he will be leaving the Primera Division side.
Juventus, who Celtic play next in the Champions League, and clubs in England have been linked with Llorente, who scored 24 goals last season to help move Marcelo Bielsa's side to the final of the Europa League.
After announcing his decision to leave, Llorente has been used sparingly by Bielsa this campaign, scoring just twice in 16 matches, the majority of which have come as a sub.
His lack of goals has seemingly done little to put off Juventus – who are eight points clear at the top of Serie A and on course to retain the title.
"Juventus informed Athletic Club on January 3 that, knowing Fernando Llorente will end his stint at our club on June 30, 2013, they will begin negotiations with the player to incorporate him into their squad," a Bilbao statement read.