The 28-year-old Brazil-born Spain international signed for £32million from Atletico in July 2014, agreeing a five-year contract, and wishes to return to the Spanish capital.
Speaking from his native Lagarto earlier this week, Costa criticised Chelsea and head coach Antonio Conte.
Costa claims he was told he was not wanted by a text message sent by Conte during the off-season.
But the Blues insist it was decided in January, with the striker and his agent, Jorge Mendes, that Costa could leave this summer.
As a consequence, Costa has been ordered by Chelsea to return to London, get himself match fit and make himself available for selection, as he still has two years remaining on his contract.
Costa met with Milton Dantas, the president of the Sergipe Football Association, and afterwards reiterated his desire to return to Atletico. Sergipe is the region of Brazil where Costa is from.
In a statement released by Federacao Sergipana de Futebol and published by O Globo, Costa said: “My destiny is already set. I must return to Atletico Madrid next season. There happens to be an impasse as Chelsea do not want to release me.
“But I believe this situation will be resolved upon my return to Spain.”
He did not say when he would be returning to Spain, but his preferred move is complicated by Atletico’s transfer embargo, which forbids them from registering new players until January.
Costa has not yet contacted Fifa, football’s world governing body, over his concerns. And FIFPro, the global players’ union, is yet to by contacted by Costa.
But FIFPro has general concerns about the trade of players through transfers.
A FIFPro statement said: “We strongly believe that players at every level of the football pyramid should have the same right as workers in other industries to follow the career path of their choice.
“A footballer’s career should not be tied to a transfer market which has spirraled out of control.
“FIFPro is not in a position to comment on the specifics of the situation of either Diego Costa.
“However, we are aware of repeated instances of the financial interests of clubs interfering with the short career of players.
Meanwhile Tottenham look set to run out in front of a near Premier League record crowd for their first home match at Wembley against Chelsea on Sunday, but have not been able to put tickets on full general sale at the 90,000-seater national stadium.
Spurs have relocated Wembley, where they played last season’s home Champions League fixtures, while White Hart Lane is being redeveloped, a project which eventually see the north London club return to a new 61,559-capacity venue.
Brent Council has allowed Tottenham to use Wembley’s full seat allocation of 90,000 for every home match, but restrictions have been put in place on the Chelsea fixture following discussions with the stadium’s Safety Advisory Group.
As such only those Spurs fans who were registered on the club’s database before July 1 2017 are permitted to purchase seats during the restricted general sale window, a measure which aims to prevent any away supporters from gaining access to the designated home sections at Wembley.
The current record attendance for a Premier League match stands at 76,073 when Manchester United played Aston Villa at Old Trafford in January 2007.
Ticket sales for Spurs game against Chelsea have already passed the 70,000 mark, including an allocation of some 3,000 to away fans, with still three days left before the game which is set to be broadcast live on Sky Sports.
Given the segregation which is required to be in place around the stadium, as well as the restrictions on sales the club are permitted to make, it is unlikely, though, that Sunday’s match will provide a bigger attendance than the 85,512 for a Champions League fixture against Bayer Leverkusen last season which was a record crowd for an English club.
Each Spurs match at Wembley is considered by the stadium’s Safety Advisory Group on an individual basis, with tickets for Burnley on August 27 currently available on general sale as should be those for visit of Swansea on September 16.