The Brazilian striker was believed to have been the subject of a bid in excess of £20million from the Anfield club last week - with that figure thought to be close to the buy-out clause in his contract.
However, speaking during Atletico's ongoing pre-season tour of South America, Costa said he had no knowledge of Liverpool's interest and is content with life in the Spanish capital.
"I'm well here, I'm happy here," he said. "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."
Costa scored 20 goals in 44 appearances for Atletico last season, including an equaliser in the 2-1 Copa del Rey final win over Real Madrid.
The 24-year-old has been capped twice by Brazil but did not form part of their 2013 FIFA Confederations Cup-winning squad.
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