The Spain striker has not been forgiven for flirting with other clubs during the summer transfer window and was sent to the changing room after a row.
The 27-year-old's future at San Mames was in doubt throughout the summer after it was confirmed that he was not willing to extend his deal amid speculation of a move to Juventus or the Premier League.
The Argentine trainer has not forgiven the forward for his actions, and has preferred to use Aritz Aduriz up front in recent matches.
Llorente and Bielsa argued on the training pitch before the 21-time capped attacker was sent to the changing rooms early, with the Leones coach unhappy with his performance in the training.
Bianconeri director Beppe Marotta recently confirmed that the Italian champions were still interested in Llorente, who has refused to rule out a January move.
Llorente came on late in last weekend’s match against Real Sociedad, as Athletic slipped to a 2-0 defeat away. He has scored one goal in his three Liga appearances this term.