The Spain global refused to return to Stamford Bridge for pre-season training after falling-out with the Blues, and he has been strongly linked with a return to Atletico since the start of the summer transfer window.
The loan move is close to being agreed and would begin in January and will ultimately result in the Spanish club paying £40m for the permanent transfer of Costa in the summer.
Chelsea have confirmed that they have agreed a deal to sell Diego Costa to Atletico Madrid.
This stance from Costa came after he reportedly received a text message from Antonio Conte saying he would no longer be required at Chelsea.
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The 28-year-old has not played for 98 days since he appeared for Spain in a World Cup Qualifier against Macedonia in June.
Costa was granted an additional summer break, missing the pre-season tour to Asia, but then extended his exile as relations with Chelsea deteriorated further and lawyers became involved.
He added: "Our hope is that he will resolve his situation as soon as possible and that he can compete, train and play, which is what he likes doing the most and what interests the national team".