Jose Mourinho has made no secret of his desire to bring in a top class centre forward in the summer, and his search has been narrowed down to the Spanish international.
The Blues are set to watch Costa in action for Atletico during their La Liga clash with Granada, as they look to step up their interest in the striker.
The 25-year-old has enjoyed a stunning goal scoring season in Spain, firing 30 goals in 33 games in all competitions, form which has seen Atletico move top of La Liga, and into a Champions League quarter final with Barcelona.
Negotiations may be helped by the fact that Atletico are keen to complete the signing of on-loan Chelsea goalkeeper Thibaut Courtois on a permanent basis.
There have also been rumours suggesting a possible part exchange deal which would see Fernando Torres make an emotional return to Atletico, however the La Liga side are thought to only be interested in signing young players with large sell-on-fees.
Chelsea have decisions to make over the future of all three of their strikers at the end of the season, with Samuel Eto’o, Fernando Torres and Demba Ba all likely to be moved on, meaning Costa would be the Blues’ first choice striker for next season should they land him.