The Blues are understood to have approached the Ukrainian club to discuss a deal for the 24-year-old, despite strong links with Juan Cuadrado.
The Colombian is said to be a top target for the London club, yet Fiorentina’s are reluctant to sell for any less than his £26.8m release clause.
Costa presents a more cost-effective option for Chelsea, who are talking to Shakhtar in the background.
Reports suggest that £20m is seen as the ceiling by Jose Mourinho’s side, which falls some way short of the Eastern Europeans’ £30m expectations.
Costa played alongside now Chelsea man Willian during his spell at Shakhtar, and his Portuguese duel-nationality could smooth over any issues surrounding a work permit.
Further to this, the player himself has confessed that it would be a “dream” to paly for the current Premier League leaders.