Monk survived a slow start at Elland Road and has now helped the club into the top five in the Championship table as well as guiding the Yorkshire outfit into the quarter-finals of the EFL Cup.
Klopp and Monk will go head to head at Anfield on Tuesday night, and the German has praised his opposite number as they prepare to try to guide their clubs into the last four of the competition.
The 49-year-old told reporters: "I think he is a very promising manager. I am happy for him that it works out for him like this.
"He was unlucky at Swansea and it was a good idea for him to join Leeds."
Leeds are bidding to reach the last four of the League Cup for the first time in 20 years.