Griezmann has established himself as one of the best forwards in Europe with his form for Atletico, having scored 36 goals in 72 appearances since his €30 million move from La Liga rivals Real Sociedad last year.
The France international's form has attracted interest from some of Europe's biggest clubs, including Chelsea, but the 24-year-old - under contract until 2020 - is happy in Madrid.
"I do not feel the need to play in Ligue 1, nor in the Premier League or in Serie A," Griezmann said on the Canal Football Club.
"I am in Spain – I'm happy. Life here, football, I like it all."
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Atletico face Benfica in the Champions League on Tuesday, knowing that a draw against the Portuguese side will be enough for them to top Group C.
"We want to win all our games and we'll go out to look for the win tomorrow," he said.
Benfica got the better of Atletico in their first group stage match - winning 2-1 at the Vicente Calderon - and Griezmann is aware of the dangers they pose.
"The game in Madrid was very difficult; they have great players in attack that can cause problems at any time," he continued.
"We need to be combative and try to win to secure top spot in the group.
"Now we know each other better, we are playing with confidence and we're difficult to score against. Our defence is very tight and I hope it remains like that."