Spanish media have claimed that a deal is close for the 27 year old, with Jose Mourinho finally about to get his man at last.
The deal is reportedly set to be around the £30 million mark, with Costa keen to get the deal over the line, after an awful World Cup with Spain.
With Costa leaving for Chelsea, Atletico boss Diego Simeone is targeting Alvaro Negrado at Manchester City.
According to the Daily Express, Manuel Pellegrini is willing to part with the Spanish striker.
Negrado won his first League title in England, but has flattered to decieve at the club, scoring his last goal in the League Cup win over West Ham in February.
He found himself behind both Aguero and Dzeko at City towards the back end of the season.
By Ben Reardon