Griezmann will depart Atletico after five years, with the France international and World Cup winner linked to LaLiga champion Barcelona, having turned down a move to Camp Nou last year.
It is set to be a busy off-season for Atletico, who will lose captain Diego Godin, Lucas Hernandez and Griezmann, while there is uncertainty over Rodri, Filipe Luis, Juanfran and Diego Costa.
CEO Gil Marin called on the squad to step up next season amid a period of change, with Atletico coming off a runner-up finish in LaLiga this term.
"[We need] players totally committed to the project, in which the group is above any individuals, as we aim to compete at the highest level as we have been doing all these years," Gil Marin said via the club's website. "Players who have abandoned our club will be replaced by players of the maximum level in order to continue competing and achieving the club's objectives.
"It is important that some players who have been in the shadow of the dressing room take a step forward and assume a leading role.
"Those who arrive will have to adapt quickly to the way we understand football.
"We need our group to be made up of players who want to be here and feel proud of wearing this shirt and this should weigh more than the ambition to earn more money."