The Spain striker’s lawyers were in Madrid on Wednesday along with Chelsea lawyers thrashing out a deal, and with the Spanish transfer window shutting an extra 24 hours later than the English, Atletico are still confident the transfer can be clinched.
But what could scupper the move is the fact that Costa owes Chelsea some £600,000 in fines for not returning for duty this summer – and the Stamford Bridge club want him to come back and pay up before a deal can go ahead.
Atletico Sporting Director Andrea Barta has rung Costa to try to persuade him to step on a plane today to smooth the way for the move.
Atletico are set to pay an initial £39m for the stay away striker, with £10m in add ons.
The two clubs were haggling over the details on Wednesday – as Chelsea prepared for what is certain to be a frantic final day of transfer dealing.
One deal that should be completed on deadline day will see Spain striker Fernando Llorente join in a deal worth around £14m from Swansea.
But Chelsea star Eden Hazard warned Belgian international teammate Michy Batshauyi that he might as well quit Stamford Bridge if Llorente arrives.
Hazard said: “Michy is now 23. If he wants to move forward, he has to play.
“If we have Llorente, Morata and Michy, it will be difficult.
“He was especially disappointed because he played a good preparation and counted on more.
“But we all know that you’ll be on the bench quickly when you’re not playing.
“As a friend, I recommend him to find a solution to play. But we have to wait for Chelsea to decide on him.
“A season like last year is not good for him and not for the national team. Because for Belgium he can be important.”
Hazard has not played for Chelsea this season after having ankle surgery this summer but could feature for Belgium tonight in their World Cup qualifier against Gibraltar.