On Sunday evening, the Daily Mail reported that Costa was refusing to leave Brazil for Stamford Bridge in order to train with the reserves after boss Antonio Conte had informed the 28-year-old that he did not feature in his plans.
The Premier League champions responded by demanding that last season's top goalscorer return to England, but Costa has backed up his previous stance, as well as suggesting that he only intends to leave West London for former club Atletico.
A statement from Costa read: "My destination is already made. I must return to Atletico Madrid.
"It turns out that there is the impasse that Chelsea does not want to release me. But I believe that this situation will be resolved now on my return to Spain."
In January, Costa was linked with a lucrative switch to the Chinese Super League, but the Spanish international was allegedly denied the opportunity to leave Chelsea due to their challenge for the league crown.