Milan and Atletico Madrid are in the running to sign Costa, who has no future at Chelsea.
Costa is not on Chelsea's pre-season tour and today was pictured training on a beach in Brazil.
The Spain international has already been replaced by Alvaro Morata at Stamford Bridge.
But Milan director Marco Fassone says his side are Billiga Arsenal Kläder - http://www.twincitiesvfp.org/Arsenal-fotbollstrojor-p-793312.cfm a long way off signing the striker.
“Diego Costa? He is Chelsea and I do not want to talk about players from other teams,” Fassone told Sky Sport Italia.
“He is a great footballer, excellent, but for now he is Chelsea.
“We are evaluating so many options, we have already done so much.
"It takes time to understand if we still have to invest in other parts of the field."
Milan have already spent over £100million on new players this summer, with striker Andre Silva arriving from Porto to lead their attack.
The spending spree comes from Milan's new Chinese owners who are determined to see the club return to Billiga FC Porto Kläder - http://www.twincitiesvfp.org/fc-porto-fotbollstrojor-p-800239.cfm the top of Italian and European football.
And Fassone insists manager Vincenzo Montella will find a way of making the new squad gel.
"We are aware of the risks of adding 10 new players to the team, but we are confident about the quality of the players and the manager to assemble them,” he said.
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