The revelation came from Atleti full-back Filipe Luis, who said his team-mate is settled at the Vicente Calderon Stadium and was comfortable pledging his immediate future to their team.
Speaking to El Mundo (h/t Metro), Luis said:
"[Griezmann] is a kid who speaks very clearly. Often players talk when they feel they are not being valued as they deserve. Then they get more attention. He would have had many offers from many teams. A player of his size wants to be up with the biggest in terms of contract and value. And that is fair as Griezmann is doing great here.
"In the end, for all the talk about other clubs, he always wanted to stay here and he is still here, happy and liking it. For sure, he can stay much longer. We hope the fans understand this and everything gets back to normal, although he has been scoring goals, and goals cure everything."
Red Devils manager Jose Mourinho could attempt to pair Griezmann with Lukaku in future transfer windows, but with the emergence of Marcus Rashford, United are well-stocked with attacking flair.
Juan Mata and Henrikh Mkhitaryan continue to fulfil the function as No. 10's, meaning Griezmann might be surplus to requirements before his potential arrival.
However, Mundo Deportivo (h/t Charlotte Duncker of the Manchester Evening News) recently reported the French star's release clause will drop from £178 million to £89 million on 1 July 2018, tempting United to go back in for his signature.
France Football highlighted the player's recent nomination for the Ballon d'Or:
France Football @francefootball
Nominee for the 2017 Ballon d'Or France Football (list of 30) : Antoine Griezmann #ballondor https://t.co/F9wprx5Sc22017-10-9 15:50:30
In other United news, Mourinho target Fabinho could be available to purchase as Monaco admitted they will find it difficult to retain the Brazilian.
Monaco vice-president Vadim Vasilyev told Bryan Swanson of Sky Sports News that he was pleased the player remained at his club this season but said the team has a "certain model" that allows talent to be sold when needed.
"He's very important, we can always count on. We are very happy that we managed to keep him," said Vasilyev.
"I think this is one player you want to keep forever. But we realise in Monaco we have a certain model, that at a certain moment when we feel it’s right we have to let players go in order to be successful again. This is not only about money; this is more about being successful."
Squawka highlighted the player's statistics:
Squawka Football @Squawka
Fabinho for Monaco in Ligue 1 since 2013/14: Most tackles won (422) Most interceptions (267) Integral part of the side. 🔐 https://t.co/xL7VmLaJJZ2017-10-12 18:22:01
Fabinho is a versatile individual but provides the benefits of a specialist at full-back and in central midfield. The 23-year-old excels in both positions and would be the perfect addition to any side fighting for silverware on all fronts.
Arguably, Fabinho's signing is more important than Griezmann's, and the steel and skill provided by the Monaco player would help take United to the next level.
Michael Carrick's career is winding down to retirement, and Fabinho would be the perfect character to inherit his position in the squad, adding a burgeoning world-class talent to the ranks at Old Trafford.