The German replaced Brendan Rodgers at Anfield in October 2015 and went on to guide the team to the EFL Cup final and Europa League final, but lost both.
Klopp is two years into his Liverpool stay and yet to win a trophy, but the ex-Borussia Dortmund boss secured Champions League qualification with his team last season.
On Saturday, the Merseyside outfit will host arch rivals Manchester United at Anfield in the lunchtime kickoff on the back of just one win in their last seven matches in all competitions.
Jose Mourinho will be the manager in the opposing dugout, but Krautzun has suggested that things could have turned out differently.
"It would be his dream to go to England one day and his favourite club would be United. That's what he said," Krautzun told The Set Pieces.
"After three or four months not working, I knew that he wanted to be in action again. When the offer came from Liverpool, I knew he would not hesitate because he wanted to get into a top club in England."
The Reds currently sit seventh in the Premier League table, seven points adrift of second-placed United.