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The English Premier League giants have been linked with the French attacker since last December and several European media have confirmed that Griezmann to United will be done in the next season.
Griezmann is one of the best football players in the world at the moment which makes him more desirable. Several clubs were keen on signing the player including Man United's league rivals Chelsea.
But if rumours are to be believed then the Red Devils are very close to rope in the Frenchman for a mammoth £85 million.
Adding fuel to the fire, Griezmann's image advisor, Sebastien Bellencontre, recently claimed that his client's move to Old Trafford makes commercial sense.
Speaking to So Foot Magazine, Bellencontre said: "When I read articles about a hypothetical transfer to Manchester United I think it would be the ideal commercial scenario.
"He would play at David Beckham's former club, which is his idol, with the same legendary number (No.7) on his back."
Griezmann idolises Manchester United legend David Beckham and he is keen to wear the iconic number 7 jersey at Old Trafford.
According to reports in France, the English giants have already agreed on personal terms with Antoine Griezmann.