Representatives of the Londoners have held a series of meetings with Costa's camp over the last month and further talks are planned around the Champions League semifinal first-leg clash between the two teams.
|THE COSTA SUCCESS
|DIEGO COSTA 2013-14 STATS
The Europa League champions are also prepared to more than triple the wages of Costa, who is believed to earn around £50,000-a-week at the Estadio Vicente Calderon.
As reported by Goal in March, the west Londoners are keen to tie up the deal before the end of the season and ahead of Costa departing for the World Cup, where he is expected to be an integral member of the Spain squad trying to defend their 2010 crown.
Atletico coach Diego Simeone cleared the way on Tuesday for Costa to leave by admitting that his side was powerless to stop him being sold to a club of Chelsea's financial might.
"It will depend on [Costa] and what he thinks is the best for his future," Simeone told AS. "I will support any decision he makes. It's natural that Chelsea are interested in him. That makes me happy because my aim and that of my coaching staff is to see our players improve.
"We understand that Chelsea have huge financial power and, if he wants to live off football for the rest of his life, I will have no problem in him going. It was like Radamel Falcao, how could I tell him not to go to Monaco?
"Samuel Eto'o is getting older and Diego Costa could do his thing there but, for now, he is ours."
Costa has emerged as Chelsea's top center forward target following a stellar campaign for Atletico, which heads the table in La Liga as well as being in the last four of the Champions League.
The 25-year-old has scored 34 times in 45 matches this season and his 26-goal league haul is second only to Cristiano Ronaldo (28).
Chelsea was keen to trigger the Brazil-born forward's release clause in January, when he was also being closely monitored by rivals Arsenal, but the player did not want to leave in midseason.
The buyout figure was understood to be £30m in January, although a slightly higher sum of £35m will need to be paid to capture him in the summer window.
The Gunners have subsequently dropped their interest in Costa following lukewarm scouting reports, leaving Chelsea in pole position to capture the prolific striker.
Jose Mourinho has made no attempt to hide his desire to recruit a blue-chip striker amid doubts over the futures of all three of the Blues' senior frontmen - Fernando Torres, Eto'o and Demba Ba. At least two of the trio are expected to leave in the summer, while Romelu Lukaku will hold talks with Chelsea chiefs when he returns from his season-long loan at Everton.
Atletico Madrid leads the chase for Torres and there is also interest in the Spaniard from Inter, Tottenham and Galatasaray. A growing possibility is that he could leave on a season-long loan to free up space in Chelsea's attack and on their wage bill.
Ba's representatives have already begun speaking to interested parties, while current first choice Eto'o, 33, is out of contract in the summer.
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