The Sun says Costa is set to move to Atletico on loan with a £35million permanent deal to be agreed next summer.
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.
Now the club have a new lease of life inside their freshly-built stadium, the Wanda Metropolitano.
Goal says 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.