The Blues could announce a deal for the 25-year-old Atletico Madrid star before the World Cup, which kicks off in his native Brazil next week.
The bustling centre-forward, who shares the same agent as Chelsea manager Jose Mourinho, has become one of European football’s hottest properties following two prolific campaigns.
Diego Costa scored 56 goals in 95 games during that spell, including 36 this season as Atletico won their first Spanish league title since 1996 and reached the final of the Champions League.
Despite being born in South America, he has elected to represent Spain, having lived and played there for seven years. He could yet be followed to Chelsea by Atletico full-back Filipe Luis.