Griezmann is a target for Barcelona.
But Costa revealed: "I think that he'll stay.
"He called me before and told me to come to Atletico. Now he won't leave me alone.
"He knows that he is an important player for Atletico.
"He is still with us and we hope it stays that way.
"I would be thrilled if he stayed, although each person has to do what's best for them.
"For me, the best thing would be for him to stay."