The Spanish striker had been tipped to stay at Stamford Bridge.
Antonio Conte is keen to add another forward to his ranks to give the Blues the necessary firepower to mount a title challenge next term.
Alvaro Morata has emerged as a target, although the west London outfit are believed to have had two bids turned down.
But according to the Daily Mirror, Atletico Madrid are refusing to leave Costa alone.
Costa joined from the La Liga giants two years ago in a £32million deal.
It is suggested Atletico are well aware of Chelsea’s interest in Morata, as Conte is lining up a third bid worth £67m.
Other reports recently suggested Atletico will target Liverpool’s Divock Origi as a contingency option if they can’t land Costa.
Conte has already landed Michy Batshuayi from Marseille for £30m.
When addressing Costa’s future last week, Conte said: “Diego Costa is our player, he’s a fantastic player with fundamental importance. He’s very happy and is working hard.
“I’m very happy with our work, I found the players have the right attitude and they are great workers.
“I’m seeing a great attitude and great behaviour from the players and we must continue that for the whole season.”