Griezmann was understood to be Manchester United’s top transfer target for the summer.
But yesterday it emerged the interest had cooled just hours after Atletico’s ban had been upheld by the Court of Arbitration for Sport.
United are now looking at their options and hope to sign a more traditional number nine.
Griezmann is seen as a number 10 and Jose Mourinho is now hoping to sign Romelu Lukaku from Everton or Andrea Belotti from Torino.
But Spanish radio station El Partidazo de COPE have claimed that Griezmann made contact with Manchester United yesterday.
Antoine Griezmann is set to stay at Atletico Madrid this summer Manchester United fans suggest Antoine Griezmann alternatives Thu, June 1, 2017
Click to reveal who Man Utd fans want to sign if a deal for Antoine Griezmann doesn't happen
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And it is said Griezmann told United he wanted to stay at Atletico following the transfer ban which would mean the club would be unable to buy a replacement if he was sold.
Atletico had lined up a deal for Alexandre Lacazette and were linked with Diego Costa.
But now Griezmann looks set to stay and United are ready to make a player-plus-cash offer including Wayne Rooney to win the race to sign Lukaku.
The Everton striker worked with Mourinho at Chelsea but had a turbulent relationship with him.
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Antoine Griezmann posted a message to Atletico fans on Instagram
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However Mourinho appears ready to bury the hatchet and work with the striker again.
Griezmann also posted a message on Instagram last night with the caption 'Now more than ever' alongside a picture of him celebrating his goal against Leicester.
Griezmann, 26, had recently said there was a 6/10 chance he would join United and admitted he was ready to leave Madrid to win trophies.
But he appears to have back-tracked and decided to stay put following the club's transfer ban being upheld.
Yesterday Madrid claimed to have been disrespected by CAS.
"This resolution is unfair and represents irreparable damage to our club," Madrid said in a statement following the annonucement the ban had been upheld.