The Anfield club recently tried to buy Costa for a reported fee of £21.8m.
But the striker, who scored 20 goals in 44 matches for the Spanish club last season said: "I'm well here, I'm happy here.
"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 our 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."
Atletico's sporting director Jose Luis Caminero has reiterated the club's stance on the 24-year-old.
Caminero said: "Diego Costa is a very important player for Atletico, we value him very highly and we are convinced that this year he is going to score a lot of goals with Atletico. He is an idol for the fans."
Pressed on whether Costa would stay at he club, he added: "Yes, he's going to continue."