As relayed by AS, Onda Cero's Radio Estadio claim that Los Colchoneros will pay an initial €45m (£41.1m, $52.9m) to re-sign Costa with an additional €10m potentially due in add-ons.
Such a total figure would appear to match Chelsea's £50m asking price, although one sizable caveat comes with the suggestion that Atletico will not sanction the deal until the Spanish international and his current employers have resolved their well-publicised differences.
Costa was given an extra week off in order to sort his future earlier this summer, although has since remained in his native Brazil while disobeying requests to return and racking up sizable weekly fines.
The 28-year-old, unhappy with a text message from manager Antonio Conte that confirmed he was not in Chelsea's plans for the new season, claims to have been treated "like a criminal" and does not want to be forced into training with the reserves.
There has been talk of legal action on both sides and earlier this week the AWOL Costa, who says he is prepared to stay in South America without playing or being paid for a whole year if necessary despite ambitions of featuring at the 2018 World Cup, gave another interview to ESPN Brasil in which he insisted that Chelsea were effectively pricing him out of a return to Atletico.
"My agent said that Chelsea want something that Atletico can't get near," he said. "When we heard that Conte didn't want me anymore, my agent went to find out if there was interest from Atletico for me coming back. Of course for the warmth and respect that I earned there, they showed interest. But they wouldn't pay a fortune. Atletico is a team growing every year, a big team, but they can't pay an extraordinary amount."
Costa claims to have rejected several other offers as he focuses on securing a third spell with Atletico and believes his achievements at Stamford Bridge should allow him to choose his next destination.
Chelsea's position remains that they want Costa to report back to west London for training, although Conte could not contain his laughter when pressed on the subject during a pre-Tottenham Hotspur press conference held at Cobham on Friday (18 August).
"It is great," he joked. "I can tell you that everyone who works in Chelsea knows very well what happened with him last season. It's funny, this interview. I'm not interested to continue this issue. For me, he's the past."
Unless a short-term loan deal is agreed, then Costa returning to Atletico would mean that he is unable to play again this year. That is because the La Liga giants are currently subject to a transfer ban that prevents them from registering any new players until January 2018.