The highly-rated forward has impressed for Atletico Madrid since joining the club from Real Sociedad in 2014.
Griezmann told Radio Monte Carlo: “[My career], in this moment, passes through trying to go as far as possible in the Champions League and winning the European Championship.
“I only think about that and I have no desire to leave Atletico.”
The 24-year-old has recently been linked with the likes of Manchester United, Chelsea, Arsenal and Bayern Munich.
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Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.