Should he move back to Atleti that he would have to sit out the first half of next season, Diego Simeone's men having been banned from registering new players until January 2018 after breaching transfer regulations.
The Spain worldwide wants to leave London and manager Antonio Conte wants him out, making this clear with a personal text message to the striker to inform him he was not part of plans for the future.
Costa had a phenomenal spell with Los Rojiblancos, helping them win the La Liga and the Copa del Rey.
"Right now I'm a Chelsea player because I have a contract, but the coach does not want me there".
However, Barcelona found that action impossible when they signed Arda Turan with the Turk forced to sit out six months until the club could register players.
It leaves Costa seemingly content to remain on the sidelines until January in order to secure a reunion with a side he has previously scored 54 goals in 114 appearances in all competitions.
"It would be nice to go back, but it's hard to go four or five months without playing and it's a World Cup year". He is not expected to be given a place in the first team, and would only be with the club during training.
The 22-year-old, who joined Chelsea's academy at the age of 10, was sent out on six loan spells before the Italian boss made a decision to keep him at the club at the start of last campaign.