Klopp will be well aware that his side can not afford any below-par performances in the Champions League.
Liverpool are second after two games on three points, above Paris Saint-Germain on head-to-head.
Leaders Napoli have four points ahead of their trip to PSG on Wednesday.
Meanwhile, Red Star look destined to finish bottom, with just one point from their opening two games.
Liverpool will travel to Belgrade after the home tie with Red Star, before going to PSG and hosting Napoli in their final Group C match.