The party from the Spanish side arrived yesterday with the intention of holding discussions with Blues director Marina Granovskaia.
Atleti are under a transfer embargo until January 1 2018 but could strike a deal in principle ahead of the winter window.
They have already agreed to pay the madcap forward £9.1m-a-season.
And the La Liga side are ready to up their offer to £32m.
The Express say sources close to the player hope a deal can finally be struck in the coming days.
Costa has been in self-imposed exile in his native Brazil throughout the summer.
Blues boss Antonio Conte told Costa he was surplus to requirements at the end of last season.
All summer he pushed for a move to Atleti but a deal could not be done.
There was plenty of talk that he might be bought by the Madrid side and loaned out until he could be registered for them in 2018.
Chelsea made a mess of their summer business with a number of top targets snubbing the champions for moves elsewhere.
And Conte admitted it was not ideal.
He said: “It’s very difficult.
“We have to wait until the end of the season and then we’ll see.
"Then I can reply very well to this question.”
