Griezmann is Manchester United's number one transfer target this summer and the Atletico star has publicly stated he would be open to a move.
On Monday, the France international said the chances of a move to United were "six out of 10” on French TV.
The following day, Griezmann told French newspaper L'Equipe that he was ready to go and win trophies.
But the 26-year-old has now appeared to suggest he wants to stay at Atletico and win trophies with them.
Man United fans expect Antoine Griezmann deal after Europa League triumph Wed, May 24, 2017
Manchester United fans are expecting the club to sign Antoine Griezmann after securing Champions League football by winning the Europa League
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It's been a great year and I hope I can get better every year and win trophies with this team
"It's been a great year and I hope I can get better every year and win trophies with this team," Griezmann told Atletico's Twitter page.
"I will do everything possible.
"We are very happy. We reached our objective, we maybe wanted more, but it could not be. We achieved the objective. We have new goals for next year."
Manchester United target Antoine Griezmann now wants to stay at Atletico Madrid
United's chances of a signing Griezmann received a major boost last night when they won the Europa League, thus ensuring qualification for the Champions League.
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After the 2-0 win over Ajax in Stockholm, Sweden, United boss Jose Mourinho was reluctant to speak about Griezmann out of respect for Atletico.
"I do not want to talk about Griezmann because that would be disrespectful to his club, Atletico," he told BeIN Sports.
"Just how I do not like others talking about by my players, I'm not going to talk about Antoine either."