The France forward, voted Euro 2016's player of the tournament, also praised the impact Atletico boss Diego Simeone has had on his career amid reports the player could leave this summer.
Chelsea, Arsenal, Manchester City and Manchester United have been linked with a move for 25-year-old Griezmann.
But he told Fifa's website: "I feel great at the club and in Madrid."
He added: "On a personal level I'm very happy, and in football terms we're about to move to a new stadium, which is very important.
"Simeone has changed me. He's brought so many things to my game. I wouldn't have been regarded as one of the best players in the world if it weren't for him.
"We'll just have to see what the future brings, but for now I'm very happy here and I hope to win trophies with this club."
Griezmann joined Atletico in 2014 for a reported £24m from fellow Spanish club Real Sociedad, who signed him as a 14-year-old.
Speaking to French radio station RMC on Tuesday, Griezmann said that, if he were to leave Madrid, he would prefer to stay in Spain.
"Who knows how the season will finish? If it finishes badly, maybe I will ask myself the question, but then where would I go?" he said.
"In Spain, Barcelona have Lionel Messi, Neymar and Luis Suarez, and a move to Real Madrid would be impossible because I play for Atletico.
"Germany is not a league that appeals to me, France, not right now, and as for England, I do watch the Premier League but I have doubts about the lifestyle. Rain, bad weather, I need to be happy off the pitch.
"I like the style of play in England and that the referees let the game flow and the grounds are always full, but the Spanish league is better suited to my style of play."
Antoine Griezmann has distanced himself from a Premier League move by saying he is happy at Atletico Madrid.