It seems to be a matter of time before the Euro 2012 winners leave their current club as they have been omitted from the squad for Sunday's Liga opener
Martinez appears to be on his way to Bayern Munich as the Bundesliga side are ready to pay the versatile midfielder's €40 million buy-out clause.
Llorente, meanwhile, recently announced that he will not sign a new deal with Athletic, and is being heavily linked with a move to Juventus.
Both players were jeered by Bilbao fans during Friday's training session, and head coach Marcelo Bielsa has therefore opted to give the duo the weekend off in order not to disrupt the preparation for Sunday's clash.
Martinez, 23, has made over 200 official appearances for Athletic Bilbao since joining the club from Osasuna, while the 27-year-old Llorente came through the ranks of the club's famed youth academy.