The World Cup winner mulled over his future last year before signing a contract extension with Atleti, having revealed his desire to stay in a documentary-style video.
Suggestions the France international could still end up at Barca persist, though, with Atletico 10 points adrift of Ernesto Valverde's side in the La Liga title race.
"I'm already used to it and a little bit fed up, every year it's the same, so I'm used to it," he told Univision when asked about the Barca speculation.
Atletico face Barcelona next month but the chances of them winning the title now appear slim.
Atleti had beaten Juventus 2-0 in the first leg but then suffered a 3-0 loss in Turin, which dashed their hopes of reaching the final in their own stadium.
"It was a bit hard [to take]," Griezmann admitted.
"But I've always been confident. I know the team needs me and now we have to do a good end of the season."
Griezmann’s decision to remain focused on the present, rather than the future, has the support of his international colleagues.
Fellow World Cup winner Samuel Umtiti, who is already on the books of Barcelona, has told Telefoot of the speculation which continues to surround a 28-year-old frontman: "I know Antoine is very happy in Madrid, it's going well for him, it's a team that plays for him, and after that, in a career there are choices that we can take and that we can regret.
"But I know he feels good there. He could play in any club around the world because of his qualities, whether in Barcelona or elsewhere, and be happy and successful."