Atletico reported Barcelona to FIFA last week over their alleged transfer pursuit of the France star after Camp Nou director Guillermo Amor said it was possible Barca president Josep Maria Bartomeu "had a meeting with Griezmann's family".
The 26-year-old forward was heavily linked with a move to Manchester United before the start of this season but opted to stay with Atletico.
Head coach Diego Simeone recently stoked speculation by saying he would not stand in Griezmann's way should he desire a new challenge, but Atletico chief executive Miguel Angel Gil Marin has sounded a more combative tone.
"Atletico doesn't want to sell Griezmann either now or in the summer," he told Mega. "For us he is a very important player, who has grown a lot and we have grown up with him.
"Our intention is to keep growing all together. Last summer we made an effort beyond the possibilities of the club and we'll do it again next summer.
"Griezmann departure isn't in our hands, but until summer is impossible to leave us."
Atletico will be able to pair Diego Costa with Griezmann in attack in the new year, when their FIFA player registration ban is lifted.
Gil Marin conceded putting together that all-star forward line has been no easy task, making him keen to renegotiate Griezmann's contract, which runs until 2022 and contains a release clause of €200m until July next year when it will become €100m.
"It's been hard for us to get Griezmann and Diego Costa together and I think it's going to be very good for Atletico," Gil Marin added.
"Until July 1, Griezmann's release clause is €200m."