Griezmann is the latest player linked to Barca as the Liga giants seemingly prepare to replace Neymar, who is set to join Paris Saint-Germain in a world-record transfer.
The France international extended his contract at Atletico in June, signing on for an additional year to take his deal through to 2022.
After his side edged Napoli 2-1 at the Audi Cup on Tuesday, Juanfran played down suggestions Griezmann would move.
"We are open to the market. It is getting a little crazy and any operation can affect you," he said, via AS.
"Griezmann is happy at the Atleti and we want to give everything for the Atleti."
Atletico came from behind against Napoli as Fernando Torres and Luciano Vietto struck late to send them into the final, where Liverpool await.
Juanfran said reaching the final of the pre-season tournament had been a goal for Atletico.
"It's a sign of identity, the coach [Diego Simeone] has instilled it. We always want to win, give our best and the fans will be proud of us because we want to win," he said.
"Now we play the final of the Audi Cup, which is what we wanted."