The Spanish international has been frozen out by Blues boss Antonio Conte since the end of last season and has been in his native Brazil ever since.
Marca are now reporting that he may now have an escape route from Stamford Bridge with Atletico agreeing a £54million fee for the controversial striker.
Costa would move in January when the Spanish club’s transfer ban has been lifted and will put an end to the long-running feud between the attacker and the Blues.
SunSport revealed how Costa was preparing to move back to Madrid by sending his family back to the Spanish capital.
Costa’s house is near the Blues’ training ground, where he was expected to report back after his summer holidays in Brazil.
But Costa refused to return despite being included in their Premier League squad.