The Croatian side were beaten in every match of last season's competition and are staring at the same fate this year, which would equal Anderlecht's record of 12 consecutive losses.
Their humiliation is compounded further by the fact they have yet to even score a goal in their five matches and have shipped 13, a run that has meant they are guaranteed to finish bottom, with tomorrow's opponents on four points.
Yet the mood in the camp remains positive, according to striker Fatos Beqiraj, who is confident they can end their barren run.
"The atmosphere in the team is very good and we cannot wait for the game," the Montenegro international told the club's official website.
"It's time to win the first points and I hope that we will succeed. Everyone who plays will give their best. It will be hard, but if we all give 100 per cent then we will get the result."
Dinamo will be near full strength with Krunoslav Jurcic, who replaced Ante Cacic as coach last week, confirming only Ivan Peko will miss out due to injury.
"We all know the circumstances for this match and I can assure you that my players will give their utmost in order to score points," said Jurcic, who is in his third spell as manager of the club.
Oleh Gusev's early header and a Josip Pivaric own goal settled matters in Zagreb's favour when the two teams met in Kiev in October.
But it has also been a campaign to forget for the Ukrainian outfit, who have picked up just one more point from their other four matches - a goalless draw at home to FC Porto.
Dynamo midfielder Niko Kranjcar has been robbed of the opportunity to play against the club with whom he began his professional career due to injury but has made the trip to Zagreb as he anticipates a decent encounter.
"I just hope that it will be a good match which will be fun for the football players and fans," he told the club's official website.