Sky Sports News reported on Monday night that a £32m fee had been agreed between the two clubs.
Diego Costa scored as Atletico knocked Chelsea out the Champions League at the semi-final stage.
If true, Jose Mourinho has done a brilliant piece of business, bringing a world class striker to complete the Chelsea jigsaw which was not yet complete.
Diego Costa could complete the move before heading off to the World Cup with Spain.
Atletico Madrid still have a final day title showdown as well as a Champions League final to play.
Sky sources: Chelsea agree £32m fee with Atletico Madrid for Diego Costa #SSN
— Sky Sports News (@SkySportsNews) May 12, 2014