They thrashed AS Roma 6-2 on aggregate on Tuesday to become only the second Ukrainian team to reach the quarter-finals after Dynamo Kiev's run to the semis in 1999.
While Barcelona are the only other side definitely in the March 18 draw for the next round so far, the likes of Real Madrid, Manchester United and Chelsea could lurk as possible opponents if they get through their last-16 ties.
"There are some very great names [potentially] in the quarters and I can tell you in advance that any of them would be pleased to be drawn with Shakhtar," club owner and Ukraine's richest man, Rinat Akhmetov, told reporters on Wednesday.
"But I would like them to regret it later."
Players from the South American country, like 22-year-old attacking midfielder Willian, have netted 12 of Shakhtar's 18 goals in their last eight Champions League games.
"We have young and talented players. They are very fast and have a great future," Mircea Lucescu, the fast-talking Romanian who has been Shakhtar's coach for six years, said.
Brazilian playmaker Jadson (pictured after scoring in Rome) has become Shakhtar's top striker with 16 goals in all European competitions.
Captain Dario Srna has long been chased by Europe's top clubs but the Croatia midfielder has opted to stay with Shakhtar where at 28 he is one of the team's oldest players.
Defender Dmytro Chygrynskiy became Ukraine's most expensive player after a 25 million euros switch to Barca.
"We have set a goal to get to the semi-finals," he said. "Others [rival teams] may have big traditions, but we have big ambitions."
