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."
The Shakhtar team, based in the gritty eastern mining town of Donetsk, is built around a group of young Brazilian midfielders and forwards bankrolled by billionaire Akhmetov.
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.
Willian, who took three years to adapt to the Donetsk climate, curled in two goals at the freezing Donbass Arena on Tuesday to help Shakhtar romp to a 3-0 victory on the night.
BIG AMBITIONS
Other Brazilian signings include Douglas Costa, 20, who joined the club for six million euros [$8.33 million] from Gremio and scored against Roma at the Stadio Olimpico to help give Shakhtar a 3-2 advantage in the first leg.
Brazilian playmaker Jadson (pictured after scoring in Rome) has become Shakhtar's top striker with 16 goals in all European competitions.
Lucescu also relies on east Europeans, especially at the back.
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.
When the Ukrainian failed to find a regular spot at the Spanish champions, Akhmetov bought him back for 15 million euros last year to cement the centre of defence.
Shakhtar would love to emulate their 2009 UEFA Cup triumph, where they beat Werder Bremen in the final, but Akhmetov refused to look too far ahead.
"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."
