Klopp, the Liverpool manager and former Dortmund coach, has a history of run ins with match officials and is facing charges from the English Football Association for his rant at referee Paul Tierney following the explosive end to Liverpool's 4-3 Premier League win over Tottenham at Anfield on Sunday.
Speaking with German football magazine Kicker on Thursday, Klopp said the idea of a coach formally challenging a contentious call has worked in other sports.
"A challenge would be a solution to avoid something like that happening again in the future," Klopp said, calling it "an interesting idea for football."
"There are many good examples of how this can work", saying "in field hockey, for instance, the challenge has long proven its worth."
American football allows coaches to challenge calls during the game, along with the NBA and other sports such as rugby league, while tennis allows players to review umpire calls.
In Germany, a refereeing decision last Friday could have cost Klopp's former club Dortmund top spot in the Bundesliga.
In the match at Bochum, forward Karim Adeyemi was taken out in the box by defender Danilo Soares. Referee Sascha Stegemann waved off the incident and it was not reviewed.
Stegemann and the German FA admitted on Saturday that the call was wrong. The referee said: "In retrospect, I have to say that I would have been happy (to award a penalty) if I had watched it again."
Dortmund ultimately drew the game 1-1, ceding their spot atop the Bundesliga table to Bayern Munich with four games remaining this season.
Klopp, who was Dortmund's coach the last time the side won the Bundesliga in 2011-12, said telling Stegemann to review the incident "was the least the VAR should have done."
Klopp said he "no longer understood the world" when seeing the incident and learning a penalty was not awarded.
In England, Klopp is in hot water after he suggested referee Tierney was acting against Liverpool following Sunday's game
The FA responded by charging Klopp with misconduct saying his words "imply bias, and/or question the integrity of the referee, and/or are personal/offensive, and/or bring the game into disrepute".
