Chelsea will trigger Costa's £32 million buyout clause to prise him away from Atlético Madrid, who are braced to lose a second coveted striker in the space of a year, following Radamel Falcao's move to Monaco.
Costa, 25, scored against Chelsea in the Champions League semi-final last month and has spearheaded Atléti's stratospheric surge to the top of La Liga. The club could win their first title in 18 years at Barcelona on Saturday, a week before their European Cup final with Real Madrid in Lisbon.
Costa has been superb for Atlético this season, offsetting the loss of Radamel Falcao
With Costa set to sign for Chelsea before the World Cup, Mourinho will be saddled with five strikers when Romelu Lukaku returns from his fruitful loan spell at Everton. At least two out of Lukaku, Samuel Eto'o, Fernando Torres and Demba Ba will be culled.
And speaking of culls, Chelsea's Brazilian contingent is set to shrivel, with Oscar touted for a potential transfer and David Luíz about to join Barcelona.
Luíz is so untrusted by Mourinho defensively he has hardly played at centre-back this season, whereas Barcelona's defence is so bad it makes Liverpool's look watertight. The only difference is one of those two teams could still win the league.
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Liverpool bid £20m for Southampton midfielder Adam Lallana on Monday, yet the Saints are holding out for £25m, according to the Echo.
The Mail add Lallana's Southampton teammate, Luke Shaw, will join Manchester United before the World Cup.
Mats Hummels has predictably emerged as a contender to replace Rio Ferdinand at United, in the wake of the former England defender's release.
Sir Alex Ferguson scouted Hummels - as well as Shinji Kagawa and Robert Lewandowski - at the German Cup final two years ago.
Ferguson cast his eye over Hummels two years ago
Julian Speroni was voted Crystal Palace's player of the season, however the goalkeeper could lose his place to England's No.4, John Ruddy, say the Telegraph.
Tom Ince has been linked with clubs varying from Liverpool to Cardiff to Monaco to Tottenham, and now the Mail have suggested Internazionale - where his father played between 1995-97.
The 22-year-old, who played on loan at Crystal Palace from January, is out of contract at Blackpool this summer.