Griezmann – who considered his future before recommitting to Atletico prior to the 2018 World Cup – has reportedly emerged as a target for Barca.
Atleti is 10 points adrift of Barca, having crashed out of the Champions League and Copa del Rey this season – leading to speculation over his future in Madrid.
Griezmann's sister, Maud, however denied contact with Barca as the 27 year-old France forward prepares for the international break.
"It's tiring to read new things every day about what my brother would think and about whoever says he knows what he's thinking," she told L'Equipe. "The only people who have been managing my brother's interests for two years are myself, my father, Alain, and our lawyer, Sevan Karian.
"Antoine is this week with the France team, which he wants to honour, as with each selection, and it is for now the only thing he thinks. I'm travelling to the other side of the world, and I can assure you that nothing is happening right now.
"That's right, Antoine is disappointed by this elimination, since one of his objectives while staying at Atletico was to win the Champions League in his stadium. But he is the same as his team-mates, coach, officials and fans.
"If there is a club we are in contact with right now, it's Atletico de Madrid and no other."
Griezmann – who has scored 18 goals in all competitions this season – will be involved in France's Euro 2020 qualifiers against Moldova and Iceland.