Chelsea are believed to be in the market for reinforcements this January, with Juan Cuadrado another apparent target as they look to consolidate their position at the top of the Premier League.
And Costa has now appeared to confirm that talks between the Blues and the Ukrainian club are ongoing, whilst revealing that he would be open to such a move.
"It would be a dream to go to Chelsea and is a unique chance for me," he told Globo Esporte. "I have been at Shakhtar for five years and think it's time to leave. I will try to negotiate."
Costa, who joined Shakhtar from Gremio in 2010, has made 17 appearances in all competitions this season, scoring twice and providing five assists.
The Brazil international attracted interest from across Europe when he left Gremio, with a number of English clubs - including Manchester United - losing out in the race to acquire his signature.
