The France international was tipped to quit the Spanish giants last summer and head to Old Trafford.
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However, Griezmann opted to stay at Atletico after the club were hit with a transfer ban.
The striker has impressed again under Diego Simeone this season, with the 27-year-old netting an impressive 27 goals in all competitions.
And according to Spanish news outlet Don Balon, Jose Mourinho is still desperate to land Griezmann.
They say the Red Devils are even willing to pay £88m (€100m) AND include a United star in the deal to secure the Frenchman.
Don Balon add that Atletico would accept the Red Devils’ offer, providing that Barcelona don’t table a bumper bid for the forward first.
However, the publication does not name which player Mourinho is willing to send in the opposite direction.
Griezmann has been vocal about his Atletico future in recent weeks, with the France star claiming he’s locked in talks with the Spanish giants.
He said: “If I’m going to continue at Atletico, I don’t know, we’ll see.
“We’re talking to the club to see what can be done.”
United are back in action tomorrow afternoon when Mourinho’s men host Watford in the final day of the Premier League season (3pm kick-off).