After reports Real Madrid forwards Gareth Bale and Cristiano Ronaldo had signed new long-term deals with the European Cup winners, Jose Mourinho has identified Euro 2016 player of the tournament Griezmann as his target for next summer.
The 25-year-old scored six goals in France over the summer as well as leading Atletico Madrid to their second Champions League final in three years.
United have grown confident of a deal as a result of the burgeoning relationship between Griezmann and Paul Pogba, who joined the club from Juventus for a world-record £89m in August.
The Euro 2016 golden boot winner, who has scored 62 goals in 113 games for Atletico and said of Pogba this week: “We get on very well. It is true that the Euros has brought us closer together still.
"Paul is a really nice guy. He is it! We send messages, Snapchats. He’s really a good friend. When he plays with his club, I try to look at it to see if he had a good game or not.”
The Red Devils will have to part with a figure similar to that which they paid the Serie A champions, with United willing to pay the £88m release clause in Griezmann’s contract.
However, Chelsea are now also believed to be willing to pay the release clause as part of a £150m summer spending spree commissioned by owner Roman Abramovich.
Manager Antonio Conte is desperate to bolster his squad both defensively and in attack, with a £60m move for Juventus’ Leonardo Bonucci also in the pipeline.
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