The club officials will meet Chelsea director Marina Granovskaia hoping to finalise the transfer of the Spain striker.
Atletico, who cannot sign players until January because of a FIFA transfer embargo, are willing to raise their offer to 35m Euros (around £32m) to seal the deal.
Costa has already agreed a salary of 10m Euros (£9.1m) a year with the La Liga club, for whom he played from 2010 to 2014.
And sources close to the player, who has been AWOL in Brazil since being told he is not wanted at Stamford Bridge, say he hopes it will all be agreed within days.
With Costa in exile, Antonio Conte failed to find a replacement during the transfer window and the manager admits he does not yet know if his squad is stronger than the one that ended last season as champions.
And he has made it clear the club hierarchy will need to adopt a clear plan next year if they are to avoid getting caught up in another late dash when the deadline is brought forward next August.
Conte’s squad was not finalised until the very final moments of deadline day when Danny Drinkwater completed his move from Leicester, following Torino right-back David Zappacosta into the club on the final day.
But a frantic Thursday also saw Chelsea miss out on Alex Oxlade-Chamberlain, Fernando Llorente and Ross Barkley, adding to the list of missed targets that left Conte with mixed feelings about the club’s dealings.
Record signing Alvaro Morata, Antonio Rudiger, Tiemoue Bakayoko and Willy Caballero also came in but with key players leaving, the manager admitted it will take time before he knows if progress has been made.
“It’s very difficult,” said Conte.
“We have to wait until the end of the season and then we’ll see. Then I can reply very well to this question.”
Eden Hazard returns to the Chelsea squad for today’s trip to Leicester but Drinkwater is likely to be forced to wait for his debut, with Foxes boss Craig Shakespeare revealing the midfielder told him he wanted to quit a month before making it official.
Drinkwater’s decision to jump ship has left a bad taste with some Leicester fans and Shakespeare hinted he was disappointed at the way things had ended with one of the stars of their title-winning team.
“There’s a saying that a lot of things in football will disappoint you, but nothing should surprise you,” said Shakespeare.
“If I’m honest, I knew well before his transfer request. Danny made it quite clear that his heart was set on a move. For me to tell our fans how to react would be wrong.”
