Liverpool last week lodged a £21.8million bid for the 24-year-old Brazil international, who scored 20 goals in 44 matches for the Spanish club last season.
However, Costa says is not looking to move away from the Vicente Calderon and is keen to stay with the Rojiblancos if they want him to.
"I'm well here, I'm happy here," he was quoted as saying by AS after returning to Madrid with Atletico from their pre-season tour to South America.
"As I've been in Argentina and Uruguay I've not heard anything about this.
"I'm happy here, if the club want me to be here, I'm going to be here.
"I think that the coach (Diego Simeone) counts on all of us, not just me. He knows how important it is to maintain the squad, the fans know it as well."