A source close to the negotiations says progress is being made but “it is not sorted yet”, after a summer-long debacle between the player and his current West London employers.
Atletico are banned from registering new players before January and have so far offered only half what Chelsea want for the striker, which has been £50m. Atletico have yet to offer more than £30m.
Costa has been in self-enforced exile from the Blues since they won the Premier League title, and has made it clear he wants to rejoin Atletico after being told he was no longer wanted by Antonio Conte.
Costa, who has won two Premier League titles in three years since joining Chelsea from Atletico for £32m, is effectively on strike having refused to return to pre-season training in July.
Chelsea have maintained that the 28-year-old is expected to fulfil his contractual obligations, return to the club, train and get himself fit enough to be available for selection.
Conte has since laughed at Costa’s claims that he is being treated like a “criminal” by the champions, who have enjoyed a strong start to the season in the Premier League and Champions League.