Reports surfaced last week that the Anfield outfit had activated the 24-year-old's release clause, which stands at around £21.8 million.
But, having already lost star striker Radamel Falcao, Atletico are keen to hang onto Costa, and the club's sporting director Jose Luis Caminero dismissed reports he was on the verge of leaving.
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“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.”
Costa, who has been in South America as part of Atleti's pre-season tour, says he is unaware of Liverpool's interest and remains totally committed to the club.
“As I've been in Argentina and Uruguay I've not heard anything about this,” the striker, nicknamed 'El Guaje', told AS.
“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.”
Costa scored 10 goals and provided seven assists in 31 La Liga appearances last term. He also netted eight times en route to Atleti's Copa del Rey triumph, including in the final against Real Madrid.