Despite having led Chelsea to their first Premier League title in five years by scoring 20 goals in his debut season with the Blues, the Spaniard is eager to head back to his former club, according to Spanish newspaper Marca.
Marca reported that Costa is finding it tough to adapt to life in London, and its climate and culture.
As a result, he has reportedly contacted the Atletico Madrid directors about a move and is willing to take a significant pay cut to secure a transfer back to Spain.
"Although his season has been notable in a sporting sense, Diego Costa is not happy at Chelsea," the report published by Marca reads. "His problem is his lacking of adaptation to London, to the rainy English climate, the language and the food.
"All of these have been key in moving the striker to make contact with the Atletico Madrid directors…with one objective. To return home, to the club he arrived at at 17 years old."
However, since the report was published, Chelsea have asserted that the 26-year-old is "not for sale at any price" as he has become a key member of their line-up.