The Daily Star says the two sides are close to finalising a £50m deal.
But discussions are ongoing and set to continue ahead of tonight’s 11pm La Liga deadline, according to Sky Sports.
Costa has been AWOL in Brazil for much of the summer as he looks to force his way out of Chelsea.
Antonio Conte told the striker he was no longer in his plans.
But Atletico’s transfer ban until January makes a switch complicated and leaves Costa in limbo.