The Premier League side will host Bayern in the first leg of their Champions League last-16 tie on Tuesday.
"Personally, I have a high opinion of Jurgen Klopp," he told reporters.
Day one tactical drills— Liverpool FC (@LFC) February 13, 2019
Time for a post-training competitive game of foot-tennis...
...Firmino and Lijnders VS Klopp and Mane! pic.twitter.com/jTxdCr8E5t
"Many years ago we agreed on a collaboration together, but we ended up signing Jurgen Klinsmann instead.
"There I showed I respect him and his work a lot. It's going to be a tough task for both sides. I hope we'll come out on top."
Klopp went on to win two Bundesliga titles with Dortmund before heading to Anfield in October 2015.
And his old club are on course to beat his one-time suitors to the title this season after Bayern's poor start allowed Dortmund to surge to the top of the table, where they now lead the defending champions by five points.
Klopp's Liverpool are also battling for league honours, sitting second in the Premier League on goal difference with a game in hand on Manchester City, who are top.
As such, the upcoming Champions League clash between the two may well be seen as an unwelcome distraction from both sides' title tilts, particularly given the selection headache in both camps.
Klopp has just one senior centre-half fit and available in the form of Joel Matip, as Dejan Lovren and Joe Gomez are injured, while star defender Virgil van Dijk is suspended.
Bayern do not have a fully-fit complement either, with regular starters Manuel Neuer and Arjen Robben both sidelined with injury, with Thomas Muller also reportedly a doubt, while Corentin Tolisso remains a long-term absentee.