The two clubs are keen to do a deal, even though they are miles apart on their valuations.
Chelsea are asking for £50million, but Atletico are only ready to pay half that.
The Spaniard has been AWOL for five weeks after a text row with boss Antonio Conte.
And there has been little sign of a breakthrough in the whole tit-for-tat row.
Costa, 29, has said he only wants to play for his former club in Spain now he has no future with the Premier League champions.
But the summer-long saga is in limbo while the player refuses to bow to Chelsea’s demands to come back to England and resume training.
Costa has claimed he is being treated like a “criminal” and that he only downed tools after Conte sent him a curt text telling him he was finished at Stamford Bridge.
Chelsea are able to fine him two weeks’ wages — around £300,000 — every fortnight when there is another unauthorised absence.
Worryingly for Costa, Chelsea have got their act together after losing their first game at home to Burnley.
They beat Tottenham 2-1 at Wembley on Sunday to show they are moving on without him, with new striker Alvaro Morata showing promising signs up front.
Costa has been holed up in Brazil since July when the rest of his team reported back for pre-season training.