Jurgen Klopp's men progressed past Shakhtar Donetsk, Malaga and Real Madrid in the knockout stages to reach the 2012-13 final, before ultimately coming unstuck against fellow Bundesliga side Bayern Munich, losing 2-1 at Wembley as a result of Arjen Robben's 89th-minute winner.
Dortmund topped Group F this term, albeit only narrowly after Arsenal and Napoli also finished on 12 points.
Zenit's only win in Group G came against Porto, but that sole triumph combined with three draws proved enough to seal a place in the knockout rounds for the second time.
Dortmund, by contrast, had to win four matches to guarantee their progression – with a 2-1 victory at Marseille in matchday six ultimately proving crucial.
Klopp's side are now 20 points behind leaders Bayern following the champions' 4-0 win at Hannover on Sunday, and a point adrift of second-placed Bayer Leverkusen.
Zenit, meanwhile, have not played a competitive match since their final Champions League group game on December 11 due to Russia's winter break and do not return to domestic action until March 9.
Luciano Spalletti's team sit top of the Russian Premier League thanks to a superior head-to-head record against Lokomotiv Moscow, who also have 40 points, but have been inconsistent in recent friendlies.
Spalletti will have a full squad to choose from barring any late fitness problems, meaning Salomon Rondon – a January signing from Rubin Kazan – could make his Champions League debut.
