The Sun say Atletico Madrid believe they will lose the striker in the summer and they’re already preparing for his exit.
Chiefs are resigned to losing the 25-year-old, with United leading the race.
“Antoine Griezmann is close to an £80m move to Man United”
The Sun add that Chelsea and Arsenal are also in the hunt for Griezmann but they look set to miss out.
They say the pair could be priced out of a move due to United’s spending power – as demonstrated by landing Paul Pogba for £89m in the summer.
An Atletico Madrid source told the newspaper: “We know now we are going to lose Antoine, it is a matter of when not if.
“The club are hoping they can keep him and Diego Simeone for one last season, going into the new ground.
“It is going to be tough, though, as some big clubs around Europe are looking at buying him for a lot of money.”