The 22-year-old, who would fulfil Athletic's Basque-only requirements having lived in San Sebastian since the age of 14, was reportedly being considered as a replacement for midfielder Ander Herrera.
However, Herrera's proposed switch to Manchester United collapsed on transfer deadline day, meaning the San Mames outfit's supposed interest was never followed up.
But, when asked about the reports, Griezmann simply emphasised his happiness with life at Real Sociedad.
"I have no idea why, I do not know who published that," the former France Under-21 international said.
"I am here enjoying my time with La Real. I have not received any calls from anyone at Athletic, I have been spending these past few days with my brother.
"And if they call, you know what my answer will be, but I do not care about that stuff. It is better for me and for Real, so that we are more focused and relaxed here."
Griezmann scored 10 goals in 34 league appearances for Real Sociedad last term as they clinched fourth place in La Liga.
He went on to score an acrobatic goal that helped his side defeat Lyon last month and seal place in the UEFA Champions League group stages via the play-offs.
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