According to reports, the Spanish club look to have managed to negotiate down the fee for the striker, with Chelsea desperate to get rid of the 28-year-old.
Atleti manager Diego Simeone managed Costa between 2011 and 2014 and turned him into a goalscoring machine at the Calderon.
According to Goal.com Simeone “has made it his personal mission” to get Costa back in the red and white stripes.
Costa would be eligible to join Atletico as of January as the club are currently in the middle of a transfer ban, according to the Sun
Costa is in Chelsea's official Premier League squad but he isn't likely to play for the club with a deal close to being agreed. He will look to find an arrangement that can see him train with Atletico Madrid until January but the fine details have yet to be fully agreed.