The Bundesliga side have travelled to Russia for the first leg of their last 16 tie and will be seen as favourites to progress to the quarter-finals, but Klopp believes his team face a closer match than many may expect.
Dortmund have displayed good form since the turn of the year, yet return to European action on the back of a shock 3-0 defeat at Hamburg last weekend.
Zenit, on the other hand, have not played a competitive match since their Champions League defeat to Austria Vienna on December 11 as the Russian Premier League takes a lengthy break to avoid harsh weather conditions.
That break could be a hindrance for the hosts, but Klopp predicts they will be fresh and ready for Dortmund's visit.
"We watched all the Zenit games we could see including training games in Israel, and all the group games," the coach said at a press conference on Monday.
"We anticipate a very strong footballing team.
"Russian football has evolved considerably in recent years. This makes it very exciting for us.
Klopp still has decisions to make regarding his starting line-up, with Mats Hummels pushing for a recall following an ankle injury.
"I think Mats Hummels will be in training and then we will decide whether he will play," Klopp added.
"(Robert) Lewandowski has been able to recover and today (Monday) he looked pretty good. He will be able to train normally."
