The France international forward spent much of the summer being heavily linked with a big-money move to Old Trafford, only to see an embargo in the Spanish capital bring an end to the rumours.
Griezmann eventually ended up committing to a new contract through to 2022 , although that has done little to curb the endless rounds of speculation regarding his future.
It has been suggested that the 26-year-old will finally depart the Wanda Metropolitano at the conclusion of the 2017-18 campaign, but Atletico president Enrique Cerezo has moved to quash such talk.
He told Marca : "We have put in a lot of effort to keep him and to keep all the players. The problem Griezmann has had is that a series of news stories about other important European clubs wanting him has not benefitted him.
"Griezmann is and will be an Atletico player. He is an important player and at an important club and he wants to win titles with Atletico.
"He may have had a start to the season which could have been better, but there is a lot left of the LaLiga season for him to show how important he is for the club and how important football is for him."
When asked about Griezmann's flirting with United in the close season, Cerezo added: "What important player doesn't play this kind of game? They all do."
Cerezo has also backed Griezmann to rediscover his best form domestically when Atletico take in a derby date with arch-rivals Real Madrid on November 18.
The Frenchman has endured a testing start to the current campaign, netting just three goals in 13 appearances in all competitions – with his last strike coming in a 2-1 Champions League defeat to Chelsea on September 27.
Griezmann did, however, find the net in France's 2-0 friendly victory over Wales on Friday and is expected to now open the floodgates.
"He hasn't had much luck at the start of this season,” added Cerezo.
“He had a fantastic end to the previous season and he is still considered one of the best three players in the world. The advantage is that he is younger and has more of a future than the other two.
"Everybody has their moments. It may be the case that he's not going through the best one right now, but I am convinced that it won't take long for him to be what we all want him to be once again, the Griezmann that he is.
"After all he has shown, there's no reason to doubt him or lose confidence in him because of playing five matches not so well.
"He will be the same old Griezmann against Real Madrid, one which is feared by defences and loved by Atletico fans."