French television station Canal Plus – who were the first to confirm Morgan Scheniderlin’s move to United from Southampton in 2015 – claimed United will this summer trigger the 100m euros (£86m) release clause in Griezmann’s Atletico contract which is not due to expire until 2021.
And they also claim Griezmann has, in principle, already agreed terms with United.
The 25-year-old forward will apparently receive the same salary as Paul Pogba – 17.7m euros a year and will wear the No 7 shirt vacated by Memphis Depay, who joined Lyon in the January transfer window.
Senior United officials have dismissed the claims but no-one at the club is saying they are not desperate to sign Griezmann, who has made no secret of his desire to move to the Premier League and line up with France team-mates Paul Pogba and Anthony Martial at Old Trafford.
Manchester United want to sign Atletico Madrid superstar Antoine Griezmann
Antoine Griezmann will demand the same wages as Paul Pogba
Apart from close pal Pogba, Griezmann's brother – a huge United fan – will no doubt be keen for him to move to Old Trafford judging by his comments on social media in recent months.
Earlier this week Mourinho confirmed he has already lined up his summer targets when he said: “We are more focused on the summer period.
“If you ask me 'do I know what I want for the next transfer window?' – yes I know. Is it possible to get? I'll try, always, to be realistic.
“I always think every week the more I know my players, the more I know my team, the more I know the competition, because it's a competition I know really well.
“But it's a competition in permanent evolution. I know what I want.”
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Antoine Griezmann has reportedly agreed a deal with United in principle
United’s need for more goals and attacking creativity was underlined in last night's frustrating goal-less draw with Hull when they blew a great chance of closing in on the top four.
Mourinho’s mis-firing team could have moved to within three points of second place but failed to find a way past Hull keeper Eldin Jakupovic, who made four superb saves.
United may be on an unbeaten run of 14 matches in the Premier League but they have drawn half of them. And, in total this season, they have drawn nine games, six at Old Trafford.
Their failure to kill off teams like Stoke, Burnley, West Ham and Hull could ultimately cost them a return to the Champions League next season.
United have managed only 33 goals in 23 League games this season – one of their lowest ever totals at this stage of a season since the Premier League was launched in 1992.
How Man United could look with Antoine Griezmann
Wed, February 1, 2017
Is this how Manchester United's squad could look with Antoine Griezmann
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Is this how Manchester United could look with Antoine Griezmann
While Zlatan Ibrahimovic – who had an off night against Hull – has got a respectable 14 League goals, no other United player has managed more than four in the League so far.
Mourinho knows that unless United’s goal output improves there is a very real danger they could finish outside the top four and that is why he is taking the Europa League so seriously because it offers a back door route into UEFA's top club competition
With Rooney's powers diminishing and youngsters Marcus Rashford and Anthony Martial both suffering "second season syndrome" Arsenal legend Thierry Henry believes Griezmann would be a perfect fit for United.
“He is someone who should come to the Premier League," he said this week. "If he goes to Old Trafford then he’ll be great for them.
“He is a player that you need [in England], for the league and the fans, to be able to see that guy. I’ve known him for a very long time. People are talking about him going to Man United – it speaks volumes of how far he has come."
Former Liverpool midfielder Steven Gerrard also thinks a move to United is right for Griezmann – once he has had a final crack at the Champions League with Atletico.
“He’s playing in the Champions League for Atletico Madrid,” said Gerrard. “He’s got a chance of competing for that, which they have done for the past couple of years.
“And he’s probably thinking: ‘Yeah, Manchester United probably is a good move, but it’s still going to be there in the summer.”