The 28-year-old, currently on strike at his family home in Brazil, was told by boss Antonio Conte at the end of last season that he is surplus to requirements at Stamford Bridge.
After seeing a mega-money move to the Far East break down in January, Costa has since made it clear that Atletico - where he has previously spent six years of his career - is the only club he will consider signing for.
According to The Sun, the Spain international recently rejected fresh interest from Shanghai SIPG and Tianjin Quanjian, both of whom were also willing to pay him around £13m to join until the New Year.
A separate report in Spanish daily AS suggests that the transfer saga is close to ending, though, as Atleti have agreed to pay Chelsea £41m up front and a further £9m in potential add-ons to get their man.
Due to the transfer ban imposed on Los Rojiblancos in June, they will not be allowed to register Costa on their books until January, but he has no interest in spending time elsewhere on loan.