During the summer transfer window, Illarramendi will see his release clause drop from €40m (£35.2m) to €35m (£30.8m), and it has allegedly resulted in interest from La Liga and the Bundesliga.
However, former Real Madrid man Illarramendi has insisted that he has no intention of leaving Txuri-urdinak ahead of the new campaign.
The 28-year-old told Diaro Vasco: "I'm happy at la Real and I don't want to play for Athletic, I don't see myself in an Athletic jersey.
"I know that I won't play for Athletic, I'm happy at la Real. How much more is €40 million than €35 million, I have no intention to move from here."
Aside from a two-year spell at Real Madrid, Illarramendi has spent his entire career at Sociedad.