According to Marca (h/t Football Espana), the deal will go through "this week," ending speculation about the forward's future.
In the same report it's suggested Atletico will pay around £54 million to bring Costa back to the capital for a second spell, although it's not yet certain how the deal will be constructed in terms of upfront payments and add-ons.
As noted by Annie Eaves of Sport Witness, Marca reported the forward has been worried about returning to Chelsea training after a summer absence, and there is now a determination on the part of both clubs to get this situation sorted.
Bryan Swanson @skysports_bryan
Fenerbahce say they've been in talks to sign Diego Costa on loan from Chelsea: "Move was close – the outcome is negative for now.” #SSN2017-9-7 20:58:23
Costa joined the Blues from the Madrid outfit in 2014 having fired Atletico to a surprise La Liga title win and the final of the UEFA Champions League.
During his time at Chelsea he has been a big hit with the club's supporters. Costa's aggressive and intense style of play is a perfect fit for English football, and it's little surprise he's been among the key men in both of the Blues' recent title wins.
While he bullies defenders and bounds after loose balls, Costa is also a fine natural footballer. Per Liam Twomey of ESPN FC, the striker scored plenty of important goals last season:
Liam Twomey @liam_twomey
Diego Costa's 20 goals directly led to 16 extra points for Chelsea in the Premier League last season. They won the title by seven #cfc2017-8-16 10:40:28
Still, Costa's Chelsea career is poised to end on a sour note. Manager Antonio Conte has opted not to use him this term, with the Brazilian-born forward spending the last three months in his country of birth instead of preparing for the 2017-18 season.
Per Football Espana, Conte is said to have sent Costa a text message ahead of pre-season confirming his career at Chelsea was over.
As noted by Miguel Delaney of The Independent, the Chelsea manager has not been keen to talk too much about his absent forward:
Miguel Delaney @MiguelDelaney
Conte stonewalls all questions on Costa: "No news"2017-9-8 12:21:40
Although Costa wouldn't be able to play for Atletico until January because of the transfer ban being served by the club, the situation being sorted soon would be to the benefit of everyone. After all, it'd be a massive surprise to see the striker train with the Premier League side again, never mind play for them.
Atletico supporters would be delighted to have Costa back, and the prospect of him lining up alongside Antoine Griezmann in attack is an ominous one for La Liga defences. After a long spell out of action, Costa will be hopeful he can still give the best years of his career to Atletico.