Manchester United manager Jose Mourinho wanted Griezmann this summer but the player was not interested in leaving Atletico Madrid.
But the France international is open to a move at the end of the season and the Daily Star Sunday claim United are ready to pounce.
According to the report, bosses at Old Trafford have already set aside the cash required to trigger Griezmann’s release clause come July.
They have also kept the iconic No 7 shirt – previously worn by George Best, Bryan Robson, Eric Cantona and David Beckham – free for the 26-year-old.
They do, however, face a battle from Chelsea to land the forward.
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The Sun claimed this week that Chelsea director Marina Granovskaia is keen to avoid the mess the club found themselves in this summer when they failed to land their top targets early.
Chelsea ended up scrambling for players and manager Antonio Conte had showdown talks with the top brass at Stamford Bridge.
Chelsea want Griezmann and are preparing their own offer for the Atletico icon.
The Daily Star Sunday add the United will not try to move for the player in January as it is too difficult a month to negotiate major signings.
But an offer will be forthcoming at the end of the current campaign.