The club are currently under a transfer embargo but will be able to sign players in the winter window.
Atletico Madrid will make a bid for Diego Costa despite their transfer ban
Costa wants to leave Chelsea after being told by Antonio Conte, via text message, that he was disruptive and no longer wanted him in west London.
According to the Daily Mirror, Atletico will make a bid of £26million – £6m less than the Blues paid for Costa in 2014.
The Spanish club plan to have performance related clauses in the bid that should see Chelsea make their money back.
The 28-year-old has scored 59 goals in 120 matches in three seasons for the Blues, winning the Premier League title twice and the League Cup.
But he has often been a controversial and divisive figure in the Chelsea dressing room.
Atletico will wait until January to bring their former striker back to the club
Diego Simeone and Costa enjoy a great relationship
Costa said that Conte has told him he wants the striker gone soon – player and manager had a huge row in January that led to Costa being dropped.
The striker still has offers to move to China but is said to have had a change of heart and now wants to return to Atletico.
However, the Madrid club are banned from any transfer deals this summer because they broke the rules over signing foreign players under 18.
Antonio Conte sent a 26-word text to Diego Costa telling him his Chelsea career was over
Atletico hope they can convince Chelsea to keep Costa until January, although Conte wants him gone before the start of the season.
The Spain international may also seek a short loan spell until January to ensure he is playing regular football ahead of the World Cup next summer.
Costa’s brother Jair said last week that he had “many offers” from clubs around the world.