Griezmann, 26, has been heavily linked with a move to Manchester United throughout this season.
It was understood that Griezmann was Jose Mourinho’s top transfer target with the Portuguese boss willing to activate his £86million release clause.
But interest in the France international has now cooled with Mourinho setting his sights on a big-money move for Everton star Romelu Lukaku.
Atleti have been handed a transfer ban meaning they cannot sign new players until January 2018.
Star players Manchester United could target instead of Antoine Griezmann Fri, June 2, 2017
Who could Manchester United sign instead of Antoine Griezmann
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Antoine Griezmann's decision to stay at Atletico Madrid has left Manchester United embarrassed.
And The Sun have offered a fresh twist on his decision to snub a move to Old Trafford.
It is claimed that Griezmann was given an ultimatum by United over a transfer before FIFA decided to uphold Atleti’s transfer ban.
The Red Devils apparently told him he should sign this summer or miss out on the chance to sign for them completely.
Antoine Griezmann has left Manchester United embarrassed by snubbing a transfer
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One reason behind Griezmann’s U-turn is because he supposedly wants to collect a £5.3m loyalty bonus at Atleti.
He is now ready to sign a contract extension with the La Liga giants and stay at the club for at least another season in a bid to hold out for more lucrative offers next season.
But The Sun say his decision has left United embarrassed with the club having a £300,000-a-week contract drawn up for him to sign.
Griezmann made 53 appearances and scored 26 goals for Atleti this season.
His current contract at the club runs until the summer of 2021.