The France international was a target for the Premier League club in the early weeks of the transfer window and was reportedly the subject of a bid of close to €100 million.
Griezmann, who was also linked with Real Madrid, confirmed he would stay at Atletico and extended his contract by a year following their FIFA-imposed ban on signing new players until January, the forward saying it would be "a dirty move" to leave the club unable to replace him.
Eric Olhats, who was the 26-year-old's agent until September 2016, says the ban is the only reason he remains an Atletico player.
"Griezmann hasn't felt able to leave Atletico," Olhats told France Football . "It showed the integrity of his links with the club, [who were] unable to sign players. Without that ban, he would have gone, without a doubt."
Olhats believes Griezmann has focused too much on trying to boost his media image since their split last year, although he says he still speaks with his former client.
"His omnipresence in the media has not helped him to relaunch himself on a sporting level," he said. "The balance between the search for performance and the desire to sell your image is very fragile. Unconsciously, you can choose the wrong side.
"There are a lot of aspects of show business in football these days. Antoine is immersed in that inescapable logic at the moment. Now, he's a footballer, not a singer.
"The press and marketing side of Antoine's career are handled by his sister Maud, who know all about that. It was decided that Griezmann's image would take a different path with new methods.
"But there's no anger or a rupture [in relations]. We speak from time to time, it’s a pause in our professional relationship, not our personal one."