Diario AS report that Costa will undergo the medical on Thursday [21 September] with Atletico ready to pay €60m (£52.9m, $71.4m) including add-ons to lure him back to Diego Simeone's side. The move is subject to the agreement of personal terms and a medical.
The 28-year-old forward has been poised to join Simeone's side after he revealed in June that Chelsea manager Antonio Conte had informed him by text message that he was no longer part of his plans ahead of the 2017-2018 season.
Costa tried to force the move during the summer after deciding to stay in Brazil despite Chelsea ordering him to report back to Cobham for first-team training.
However, the negotiations between the clubs have been complicated with Atletico being unable to register any new players until January due to a Fifa ban.
But on Wednesday (20 September) COPE said that Atletico and Chelsea had made a breakthrough in the negotiations with Los Colchoneros expecting to announce the deal in a matter of days. COPE had said that Costa will eventually land in Madrid on Saturday – suggesting that the Spain international could be a new Atletico player by the time they host Chelsea in their Champions League encounter next Wednesday [27 September]
AS have supported those claims, adding that the striker will undergo his medical in the coming hours before completing a €60m transfer to Atletico.
Costa is yet to play a competitive game since scoring in Spain's 2-1 World Cup qualifying win over Macedonia on 11 June. Atletico are not able to register him until January but Simeone wants to sign him as soon as possible so he can be 100% fit for the second part of the season.
Indeed COPE adds that the idea is for the AWOL Chelsea striker to make his Atletico debut in the first leg of the Copa del Rey last eight to be played on 3 January if Los Colchoneros progress in the competition.
Cadena Ser show El Larguero reported last week that Costa was expected to complete a three-and-a-half year move to Atletico in around "10 or 15 days". At the time Atletico president Enrique Cerezo refused to deny those reports after admitting that Los Colchoners did want to sign the Chelsea outcast.
"It's always good to hear good news like this. The truth is that we had no idea about it but one never goes to bed without knowing anything new," Cerezo joked when asked by Cadena Ser whether he could confirm that the agreement is close. "I do not deny it at all. I totally agree when journalists talk because you journalists speak well and know what you are saying. But I'm glad I came here tonight [to learn that we are about to sign Costa] because now I can go home calmer. I'm leaving home at once."
"We can not register players [until January] but we can sign. We want Diego Costa," Cerezo admitted. "Another thing is that we can bring him because there are always a number of circumstances for a negotiation to go through. If that is solved, Costa will come. If it is not solved, he won't join us."