Kjaer and the Denmark national team's medical staff were awarded the 2021 UEFA President's award after they helped save the life of Christian Eriksen, who suffered a cardiac arrest during the Danes' match with Finland in June.
Writing in his match programme notes, Klopp stated: "I am usually more keen to focus on my own players rather than an opponent, but tonight I must make an exception.
"This evening it is possible that Simon Kjaer will line up against us and this is a person who I think has the respect of the entire football and sporting world.
"You recognise true leadership in a crisis. I think the world acknowledges this now more than ever with everything that goes on around us.
"Like millions of others, I was rocked by the scenes that unfolded at the European Championships in the summer when Christian Eriksen fell ill during Denmark's opening group game.
"There were many heroes that night, not least of all the remarkable medical professionals for the Danish national team, in the stadium and subsequently at the hospital. But Simon shone that traumatic day for his own conduct.
"The image of the Danish players shielding their teammate as he was cared for will, in my opinion, forever be one of the most iconic in sporting history. It showed the best of humanity. Compassion, care and love for their friend.
"Honestly, I have no idea how he managed to not only keep his own composure in that situation, but to have the clarity of mind to make the decisions he did in that moment. His conduct humbles us all.
"I'm told that Simon's dad is an LFC fan – and if that is the case he must be bursting with pride that his boy is now recognised worldwide as the epitome of our anthem You'll Never Walk Alone.
"I know our supporters are knowledgeable and generous of spirit and therefore I am sure Simon will feel the gratitude of the home crowd tonight, but for the 90-plus minutes of the game he is again the opponent."
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