Costa, who left Atletico two years ago, struggled to find his best form as the Blues slid to tenth in the Premier League last season.
However, it has not deterred Diego Simeone from eyeing a deal to bring the Spaniard back to Atletico, who could return after missing out on a place in his country’s Euro 2016 squad this summer.
The La Liga side are desperate to land a marquee striker after losing a second Champions League final in three years to fierce rivals Real.
Club president Enrique Cerezo told GazzaMercato: “We like Costa a lot, I have to say.
“We are speaking with the player and working towards bringing him back to Madrid. We are close, but I cannot say anything more.”
Cerezo also dismissed speculation that they would swoop for AC Milan striker Carlos Bacca, who is wanted by West Ham.
Bacca is wanted by the Hammers to spearhead a new era at the Olympic Stadium, but Atletico seemingly are out of the race for his signature.
He added: “Bacca is a great striker, but we will not buy him.
“We know him and he will not enter into our plans. Bacca will not be coming to Atletico Madrid.”