It seemed as if everything was going well for Costa until Antonio Conte told him that he was not part of his plans for the next season.
The Spanish giants have seen a transfer ban upheld following a series of illegal signings of minors - something which impacted Antoine Griezmann's departure to Manchester United - and are now unable to register any players until that ban expires in January 2018.
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Costa was also heavily linked with a move to China in January.
That led to both Milan and Juventus being mentioned as possible suitors for Costa, although Juventus are in the process of signing Patrick Schick.
Atletico are reluctant to pay more than £20m for a striker who was Chelsea's top-scorer last season.
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Costa signed for the club from Atletico in summer 2014, and is only thinking about moving back to Madrid over anywhere else.
Costa, who has two more years on his contract at Stamford Bridge, is a popular figure in the dressing room but does not want to stay and a festering row between Conte and a senior player will sour the atmosphere.
Turan joined from Atletico in the summer but was ineligible to play until their ban was over six months later, meaning he was only able to train.
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Chelsea have agreed to sign Manchester City goalkeeper Willy Caballero on a free transfer which will be announced on July 1, while they are hopeful of signing Tiemoue Bakayoko for a fee in excess of £40 million (S$70.2 million).