Pepijn Lijnders has stunned Liverpool by choosing to leave this week.
The Mirror says he has left with immediate effect to join Dutch second-tier club NEC Nijmegen as the first-team manager.
Speaking on the Reds' official website, Klopp said: “It's such a strange mix of emotions talking about Pep leaving us.
“Firstly, I am gutted to be losing such a valuable member of our coaching team and such a brilliant person from our group.
“But that is tempered by the fact I am very excited for him to have this opportunity and as much as we would have loved for him to remain with us, we cannot stand in his way for what is a fantastic opportunity."