Talks have broken down between Llorente and the club over the terms of a new contract with the players apparently unhappy about the offer on the table.
There are also suggestions that he has an uneasy relationship with manager Marcelo Bielsa.
With Llorente's contract expiring in 2013, Athletic are likely to cash in before the end of August.
Club President Josu Urrutia said the rejection was an "institutional failure".
He said: “This is not a choice made over economics, but for a collection of reasons and what weighed heavily was he wanted to play in other competitions. I communicated my disappointment."
Athletic are looking for a fee in the region of 30 million Euros for the giant forward.