Manchester United are said to have already agreed personal terms with Griezmann – a £15million-a-year salary and the No 7 shirt left by Memphis Depay.
The Red Devils will have to meet the £86m release-clause in the 25-year-old's contract, which he signed last June to keep him at Atletico for the next five years.
Manchester United to free up funds before signing Antoine Griezmann
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
United re-signed midfielder Paul Pogba from Juventus last summer for a world-record £89m and is said to earn £290,000 a week – similar to Griezmann's offer.
And, according to the Independent, Jose Mourinho will be forced to sell United captain Wayne Rooney, striker Anthony Martial and midfielder Marouane Fellaini before he can bring Griezmann in.
Rooney, who is contracted at Old Trafford until the summer of 2019, has been heavily linked with a big-money move to China, which would free up £260,000 in United's weekly wage bill.
Wayne Rooney, Anthony Martial and Marouane Fellaini could all leave for Antoine Griezmann's arrival
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While Martial has struggled since Mourinho's arrival in the summer and United could be tempted to cash in before his initial £36m fee rises to £58m due to performance-based add-ons.
The Frenchman has been dropped by Mourinho a number of times this season, with the manager telling him to his step-up his game last month.
Griezmann has emerged as one of the most sought-after strikers in Europe since joining Atletico in 2014, scoring 72 goals in 136 appearances for the La Liga giants.