Chelsea hope to conclude the signing of Diego Costa from Atlético Madrid immediately after the Spanish club's participation in the Champions League final on 24 May after agreeing to meet the £31.8m release clause in the striker's contract.

The Brazilian-born Costa has been a key member of the Atlético side who can secure the Spanish title by avoiding defeat to Barcelona at Camp Nou in their final league game this weekend. The 25-year-old has scored 27 goals in La Liga this season, the most productive campaign of his career by some distance, but has been just as impressive in helping Diego Simeone's side reach a first European Cup final in 40 years.

Indeed, he scored the penalty which edged the Spanish club 2-1 up at Stamford Bridge in the semi-final last month, going head to head with John Terry in one flashpoint in the fixture and riling the home support in the Matthew Harding stand behind Mark Schwarzer's goal. The striker has long been José Mourinho's principal forward target for the close season, a player Chelsea could not hope to prise away from the Vicente Calderón mid-term, with the London club now prepared to trigger the release clause in Costa's deal.

Costa, who shares his agent, Jorge Mendes, with Mourinho, will need some persuading to move to the Premier League but is expected to be swayed. Marina Granovskaia, effectively Roman Abramovich's representative in London over the past four years and a member of both the Chelsea plc and football boards since last summer, is understood to be overseeing negotiations. Granovskaia played a key role in recruiting David Luiz and Fernando Torres from Benfica and Liverpool respectively and travelled to Madrid in April 2013 to discuss Mourinho's return to the club.

Chelsea hope to conclude the deal before Costa joins the Spain squad for the World Cup, the striker having declared himself for the holders despite making two appearances for Brazil in friendly fixtures last year. He has been playing his football in Europe since moving to the Portuguese club, Braga, in 2006 with spells on loan at the likes of Rayo Vallecano and Celta Vigo, as well as a season at Valladolid, before establishing his credentials at Atlético this term. The Spanish club, who are likely to be frustrated in their attempts to secure Thibaut Courtois on loan from Chelsea for a fourth season, will be reluctant to announce any imminent deal until the conclusion of their campaign.

Mourinho admitted after Sunday's victory at Cardiff that he expects Samuel Eto'o to depart under freedom of contract next month while doubts still surround the futures of Fernando Torres – who has interested Atlético – Demba Ba and Romelu Lukaku at the club. The manager delivered a review of the season with his recommendations on squad strengthening and tweaks to the board on Monday and will discuss its content in further meetings with the hierarchy over the next few weeks.