The Premier League leader is ready to pay upwards of 36 million euros for the Atletico Madrid striker.
Intermediaries representing Chelsea have already held meetings with the Costa camp and further discussions are expected in the next week.
|VIEW FROM SPAIN
|By Ander Bilbao - Chief Editor of Goal Spain
If Atletico Madrid President Enrique Cerezo is to be believed, the Spanish club has little intention of entertaining the sale of Diego Costa this summer. "I do not think Diego Costa is going to leave Atletico next year. We do not want any player to be a bargaining chip," he said earlier this month.
However, in admitting that "teams are coming for our players", Cerezo admitted at least the growing interest in Atletico's top stars, with rumors increasing by the day about one sale or another. Equally, the recent stories of a potential Atletico deal for Fernando Torres could have an impact on the sales strategy, while the future of Atletico's keeper Thibault Courtois - on loan from Chelsea of course - could also prove a factor. Either way, what is sure is that Atletico would not be paying as much money out for a new striker.
Costa has emerged as Chelsea's top center forward target following a stellar campaign for Champions League quarterfinalist and La Liga title challenger Atletico.
The 25-year-old has scored 31 times in 41 matches this season and his 23-goal league haul is second only to Cristiano Ronaldo (26).
Chelsea was keen to trigger the Brazil-born forward's release clause in January, when he was also being closely monitored by Arsenal, but the player did not want to leave in mid-season.
The buyout figure was understood to be €36 million in January, although there are well-sourced rumors that a slightly higher sum will need to be paid to capture the player in the summer window.
Arsenal has subsequently dropped its 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 center forward amid doubts over the futures of all three of the Blues' senior front men - Fernando Torres, Samuel 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.
As reported by Goal, 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 Torres could leave on a season-long loan to free up space in Chelsea's attack and on the 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.