The France international is understood to be the top transfer priority at Old Trafford this summer.
And the 26-year-old has dropped his strongest hint yet that he is ready to link up with international colleague Paul Pogba at United.
Atletico Madrid are braced for bids for the forward, who has been speaking on French television show Quotidien.
In an interview with host Yann Barthes, Griezmann described the chances of him joining the Red Devils as "six out of 10".
Here, the Manchester Evening News' Manchester United editor Samuel Luckhurst has the full story...
Antoine Griezmann was speaking on French television about his chances of playing for Manchester United (Photo: Quotidien/Twitter)
Antoine Griezmann à Manchester ? « Possible » répond l’intéressé, qui estime ses chances d’y jouer l’an prochain à 6 sur 10. #Quotidien pic.twitter.com/a6XuihJWVG
— Quotidien (@Qofficiel) May 22, 2017
Antoine Griezmann says there is a 60 per cent chance he could join Manchester United in the summer transfer window.
United earmarked Griezmann as the priority to sharpen their attack as early as last September and Jose Mourinho had tasked his United's French players with convincing the France international to join the club.
Griezmann's Atletico Madrid contract features an £85million release clause which United are believed to have no issue with triggering but Griezmann is understood to be insistent on playing Champions League football next season.
The 26-year-old appeared on French TV show Quotidien on Monday night and was directly asked about the possibility of joining United.
The 26-year-old appeared on French TV show Quotidien on Monday night (Photo: Quotidien/Twitter)
"My future will be decided within two weeks," Griezmann said.
When presenter Yann Barthès asked Griezmann to rate the chances on a scale of one to 10, the star replied: "Six."
Griezmann's United-supporting brother Theo retweeted Quotidien's video and appeared to endorse his comments by then posting a smiley emoji.
The Euro 2016 top scorer also spoke fondly about his idol David Beckham, revealing he got into tattoos aged 18 because of the United great's influence and copied his hairstyles, but admitted he had never met the former England captain as he 'doesn't know how to go about it'.
Griezmann is set to leave Atletico Madrid this summer (Photo: Rex Features)
Griezmann revealed he has taken plenty of inspiration from Man United legend David Beckham (Photo: Getty Images Sport Classic)
United manager Jose Mourinho has compiled two transfer lists in the event United do not qualify for the Champions League through winning the Europa League.
Another target - Monaco midfielder Tiemoue Bakayoko - is understood to be intent on playing in the competition at his next club.
Griezmann's revelation is encouraging for United boss Jose Mourinho (Photo: AFP/Getty)
Monaco midfielder Tiemoue Bakayoko is another player understood to be attracting attention from United (Photo: AFP/Getty Images)