Griezmann has been linked with a move away from the Spanish capital for the past 18 months and was on the verge of joining Premier League side Manchester United last year.
He made a U-turn, however, when Atletico’s transfer ban was upheld and instead signed a new deal through to 2022.
“He knows he’s an important player for Atletico,” Costa said yesterday.
“He’s with us now and we want it to remain that way. I would love him to stay, but everyone needs to make their own decisions. For me that’d be him staying.
“I reckon he’ll stay with us. He called me to see if I was going to join him at Atleti, he can’t leave me on my own now.”
Costa, who officially re-joined Atletico from Chelsea in January after an acrimonious falling out with manager Antonio Conte, did not play for the first half of the season.
His performances since coming back into the side, scoring six times in 14 appearances in all competitions, have earned him a recall to the Spain squad for the first time since June last year for the upcoming friendlies against Germany and Argentina.
The 29-year-old said that he was in a good place now following a difficult period.
“I’m happy off the pitch. Before things didn’t go well, but my team mates believed in me,” he said. “Everyone’s always treated me really well. I’m happy and with things like this I always will be.”
The man who replaced Costa at Chelsea, Alvaro Morata, has come in for criticism of late after going 13 games without scoring and was omitted from Julen Lopetegui’s latest Spain squad. He found an unlikely ally in Costa, though.
“I miss him because we get on well. My life’s never been easy, and I improve with competition. Hopefully he’s in the next squad. He’s having a bad time at the moment, but I hope things change for him,” the former Chelsea striker said.