Griezmann, 27, has been linked with a sensational end of season move to title-rivals FC Barcelona in recent weeks, while Manchester United are reported to be keen to activate his release clause.
But Costa, who only recently re-joined Atleti, following an acrimonious exit from Chelsea, has urged the France international to remain with Diego Simeone's side - claiming it would be in his best interests.
"He knows what we love him, that he is very important. He is still with us, I hope he continues to be. He hasn't told me yet that he is going, he knows he's important," he told reporters, as quoted by AS.
"It is his decision, I can't intervene. Everyone has to look out for the best for them and in my opinion, the best for him is to stay.
"I think that he is going to stay. Before, he called me to come back so we could play together. And now he leaves? I told him that it can't happen (laughs)."
Griezmann has been in sublime form with Los Rojiblancos this season with 23 goals and 13 assists in 38 appearances across all competitions.