The Blues have been courting Costa for some time, and reportedly view him as the solution to their striker problems.
The Brazilian-born forward has 23 goals in 28 La Liga games so far this season, and has made his international debut for Spain.
Now according to Goal, Chelsea have opened talks to get the ball rolling ahead of a summer deal, with intermediaries representing the Premier League club meeting with officials from Atletico Madrid, with more talks to come over the next few weeks.
The website add that Chelsea are hoping to get a deal wrapped up before Costa departs with Spain to play at the World Cup, where his value could sky-rocket.
Chelsea have looked short of options in attack this season, although Samuel Eto'o has started to find the back of the net more regularly in recent games.
Arsenal have previously been linked with the 25-year-old, who is currently the second highest scorer in Spain behind Cristiano Ronaldo.
It is unclear what the deal for Costa would mean for the future of Fernando Torres, who has been linked with a return back to the Vicente Calderon.
Eto'o is out of contract at Stamford Bridge in the summer and is likely to leave, while Demba Ba is another who could be on his way out.
That leaves youngster Romelu Lukaku, who is currently on loan at Everton. Previous reports have suggested that Chelsea have put him up for sale, but Goal report that he will hold talks with club officials upon his return to west London in the summer.
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