A transfer ban was imposed on Atletico Madrid in July 2016 for two consecutive transfer windows after it was discovered that they broke Federation Internationale de Football Association rules with the signing of players under the age of 18.
The ban means that Diego Simeone's transfer plans have been been thrown into turmoil, with a move for Chelsea's Diego Costa and French striker Alexandre Lacazette now seemingly off the table.
"We have chose to stay [Griezmann and his sporting adviser Eric Olhats]", he said.
"It is a hard moment for the club, for the players, and it would not be right to leave now. We talked to the leaders and we will be back for next season", said Griezmann, who explained he had discussed his decision with his advisors.More news: Ariana Grande Manchester benefit concert: How to help
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"The questions about my future have been a bit annoying".
He scored 26 goals in 53 appearances for Atletico this past season, helping the club finish third in LaLiga, and reaching the semi-finals of the Champions League and Spanish King's Cup.
It was reported in England this week that United had dropped their interest in Griezmann, as speculation mounted that he would not seek a move. You have to ask Ed Woodward.
"I've had a year off for the first time in 25 years, got a chance to do different things and I've enjoyed it, but I've always said I want eventually to be a manager or coach".
"He knows everything since March and now it is for him to work, because he will have holidays in August and in August I am working".