The Brazilian attacker featured alongside the now Blues ace when he was plying his trade in Ukraine, and the duo formed an exciting relationship in the final third of the pitch.
Chelsea are believed to be trailing Fiorentina’s Juan Cuadrado, but with La Viola holding firm with their valuation – thought to be around £26.8m – the Londoners have now put Costa on their hit list.
Reports suggest that the Stamford Bridge outfit have been trailing the tricky playmaker, now 24, since his teenage years.
Costa has been capped by Brazil, but due to duel-citizenship he holds a Portuguese passport, which will ease any problems surrounding work permits.
Chelsea are said to have entered talks at around the £16m mark, but Shakhtar are known for their tough negotiating skills and are heavily backed financially.
Costa started his career in his homeland with Gremio and joined his current side when he was 18 in a somewhat shock £6m deal.