After winning back-to-back league titles in 2011 and 2012, as well as the German Cup last year, Dortmund are now left with only Europe's premier club competition to fight for.
Rivals Bayern Munich have all but secured their first Bundesliga title since 2010 with a huge lead and eliminated Dortmund from the German Cup last eight last Wednesday.
"We have never said this is a bad season for us," said midfielder Jakub Blaszczykowski. "Obviously we want to win the championship but this season Bayern are very strong.
"The German Cup elimination is also a fact but we still have a chance to make the Champions League quarter-finals so I hope that by 11 o'clock on Tuesday evening we will all be happy."
Dortmund carved out a 2-2 draw in the first leg in Ukraine last month and look to have an advantage going into Tuesday's game.
Coach Juergen Klopp's team bounced back in style after their defeat to Bayern as they cruised past Europa League hopefuls Hanover 96 3-1 in the Bundesliga on Saturday.
Robert Lewandowski struck twice and looked unaffected by the swirling speculation regarding a possible transfer to Bayern. Klopp is also hopeful that central defender Mats Hummels, who missed the last two games due to influenza, could be back.
"At the moment I am assuming that Mats could still make it," Klopp said. "He is supposed to start running again and we will have to wait and see how it goes."
Shakhtar kicked off their season on Friday after a three-month break by demolishing FC Volyn 4-1.
Oleksandr Kucher, who was suspended in the first leg, is likely to pair up with Yaroslav Rakytsky in the central defence, replacing Dmytro Chygrynsky who has been struggling to get back into shape.
The 30-year-old centre back headed in the second goal on Friday.
Brazilian attacking midfielder Douglas Costa, who also scored against FC Volyn, might be another starter on Tuesday.
Costa came off the bench in the second half of the first leg against Dortmund and needed only six minutes to restore Shakhtar's lead on 68 minutes before Hummels headed in an equaliser three minutes from the final whistle.
"Everything will depend on players' conditions, we will analyse it," coach Mircea Lucescu told reporters.
"A goal is a solid boost to (Costa's) competitive spirit. I really push Douglas hard urging him to go into the penalty area and finish our attacks.
"This is our problem, particularly with the Brazilians; I mean entering the penalty area and converting opportunities into goals," he said.
Borussia Dortmund: 1-Roman Weidenfeller; 26-Lukasz Piszczek, 4-Neven Subotic, 15-Mats Hummels, 29-Marcel Schmelzer; 8-Ilkay Guendogan, 5-Sebastian Kehl; 16-Jakub Blaszczykowski, 10-Mario Goetze, 11-Marco Reus; 9-Robert Lewandowski
Shakhtar Donetsk: 30-Andriy Pyatov; 33-Darijo Srna, 44-Yaroslav Rakitskiy, 5-Oleksandr Kucher, 26-Razvan Rat; 3-Tomas Hubschman, 7-Fernandinho, 29-Alex Teixeira, 22-Henrikh Mkhitaryan, 20-Douglas Costa; 9-Luiz Adriano.