Frenchman Griezmann remains one of United’s top transfer targets despite the club acknowledging that getting any move over the line at the end of the season will prove difficult.
United could be willing to break the world transfer record once more to get their man but Atletico chairman Enrique Cerezo believes the Rojiblancos have now created an environment that will encourage players, like Griezmann, to stay rather than leave.
The likes of Sergio Aguero, Diego Costa and Radamel Falcao have all chosen to leave the Vicente Calderon in recent years but Cerezo hopes a new 67,000-seater stadium, coupled with the team's sustained success on the pitch, will see the club’s current stars buck that trend.
"The best players will always end up playing where they want but now fortunately we have players who want to play at Atletico," he told Reuters.
"We are doing well in the Champions League, we finish high in the league every season, we will have a magnificent stadium and we have a brilliant fan base who love all the players.
“We have everything a player could want."
Manager Diego Simeone, the mastermind behind the club’s recent successes, has been linked with a move elsewhere too but Cerezo thinks the attraction of leading the team into their new home, the Wanda Metropolitano, next season will be a factor in keeping him in the Spanish capital too.
"We have been in the Calderon for 50 magnificent years, we have won many trophies here, the best players in the world have passed through here but everything has to change at some point and that time has come," he added.