The France international endured an underwhelming debut campaign with Barca after arriving from Atletico Madrid in a €120million transfer last year.
He registered 15 goals in all competitions but was often played out of position and struggled to earn a regular place in the side in the closing stages of the season.
Paris Saint-Germain, Manchester United, Arsenal, Liverpool and former club Atletico have all been tipped to move for Griezmann, but the forward has no desire to leave Barcelona.
"Is my future is at Barca? Yes. I don't know why people invent destinations to see if one day they will be right," he told French outlet M6.
"I am very well there. I know I have the confidence of the club and the coach so I am well. It has been a very complicated season for all of us but now we start again."
Griezmann, under contract with Barca until the end of the 2023-24 campaign, scored for France on Tuesday to draw level with Zinedine Zidane as the nation's fifth all-time top scorer.
The 29-year-old has 31 goals for the world champions, putting him behind only David Trezeguet, Olivier Giroud, Michel Platini and Thierry Henry, who struck 51 times for Les Blues.