The 22-year-old joined the Ukrainian giants in 2010 and quickly established himself as a regular first-team player.
Costa has been linked with Spurs, but his agent says that he is "very happy" in Donetsk for the moment amid speculation Napoli are also tracking the player.
"The interest of Napoli and Tottenham is very pleasing," Cesar Bottega told Tuttomercatoweb.
"However, Douglas was followed more in the past, now he has lost a little appeal.
"He wasted time and is now returning to the team. But nowadays he is a reserve.
"His future? He is very happy at Shakhtar and is interested in staying there. We will see what happens later on in the future."