Blues boss Jose Mourinho is known to be in the market for a new goal-getter, and has settled on the Brazilian-born Spain international after months of deliberation.
The likes of Luis Suarez, Karim Benzema, Wayne Rooney and Gonzalo Higuain have all been mooted as targets, but it is now understood that Costa is the man ‘The Special One’ wants.
Mourinho is thought to have been impressed by the Atletico star’s excellent 2013/14 campaign, in which has netted a staggering 21 goals in 26 outings in La Liga.
Chelsea are known to have a good relationship with the Spanish club – to whom they have loaned Thibaut Courtois for the last three seasons – and could use this to their advantage.
Although £27m is some way below Costa’s release clause, it is thought that if the player pushes for the deal Atletico may reluctantly accept.
Rumours of a switch have been further fuelled by the Madrid side’s increasing interest in Porto forward Jackson Martinez.
Chelsea are said to be looking to secure a deal ahead of the World Cup – in which Costa is set to represent Spain after turning his back on his birth nation.