The France worldwide had been heavily linked with a move to Manchester United having previously rated his chances of joining the club as "six out of 10".
Griezmann himself had said that a move could be possible earlier in a televised interview with United having been ready to pay a release clause in his contract reportedly of more than 100 million euros ($112 million).
Griezmann, who scored 26 goals for Atletico last term, fuelled speculation over a summer move to Old Trafford last month when he said there was a 6/10 chance of him joining Manchester United in time for the new season.
France forward Antoine Griezmann says he will stay at Atletico Madrid next season because it will be a "dirty move" to leave the club after their transfer ban was upheld.
"I have said all season I have said that I felt good and I wanted to stay".
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Old Trafford "insiders" made claims that they chose to withdraw from negotiations over deals for Cesc Fabregas, Toni Kroos and Pedro after they failed in their bid to sign players, but it seems these leaks are little more than an attempt to win a PR war after a transfer setback. There is still a handsome season to be done and we hope to get some new signings in January.
Griezmann told French television, as quoted by BBC Sport: "It's a hard time for the club".
Both sides failed in their initial appeals to Federation Internationale de Football Association, but Real had their ban cut into half by CAS, while Atletico's suspension was upheld on Thursday, although their fine was reduced. It would be dirty move to leave now.
But, in an interview with TF1's Sunday morning programme Telefoot, Griezmann said: "The CAS sanction has come in".
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