The Red Devils secured Champions League football for next season by beating Ajax in the final of the Europa League on Wednesday.
And, according to the Mirror, the Old Trafford hierarchy now believe they have every chance of tempting Griezmann, 26, away from Atletico Madrid.
His deal in the Spanish capital apparently includes an £86m release clause.
And the Mirror say United are ready to trigger that clause.
Griezmann talked up a possible move to Manchester on French TV this week.
The France international described the chances of him joining the Red Devils as “six out of ten”.
However he has since claimed he wants to win trophies with Atletico.
Griezmann bagged 26 goals in 53 appearances across all competitions as Diego Simeone’s side finished third in La Liga and suffered a Champions League semi-final exit at the hands of arch rivals Real Madrid.
“It has been a great year and I hope I can get better every year and win trophies with this team," he told the club’s official website.
“I will do everything possible.
“We are very happy. We have reached our objective, we maybe wanted more, but it could not be. We have achieved the objective.”
