The defender helped save Christian Eriksen's life when the Danish playmaker collapsed during a clash with Finland at Euro 2020.
Kjaer has been praised for his heroics and recently received the UEFA President's Award, along with the medical staff, for his outstanding display of leadership.
Now the 32-year-old travels to Anfield in a Champions League group stage clash - and looks set to receive a hero's welcome.
Reds manager Jurgen Klopp and captain Jordan Henderson have already put the match to one side to praise their opponent.
"I am usually more keen to focus on my own players rather than an opponent, but tonight I must make an exception," Klopp explained.
"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 Championship 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."
Meanwhile, Henderson echoed those sentiments on Twitter.
In reference to his programme notes, the England midfielder said: "I'd like to welcome @acmilan's @simonkjaer1989 to Anfield this evening. He set new standards of leadership during Euro 2020 when Christian Eriksen fell ill.
"I can't even begin to imagine what that experience was like for the Denmark players and I'm hugely relieved that Christian continues to make a recovery, but as a captain I couldn't help but be impressed by the way Simon conducted himself and led his team.
"I have seen that @UEFA have given Simon and the Denmark medical team the President's Award, and that is both fitting and deserved.
"But I hope Simon also knows that he has the respect and admiration of everyone in football for what he did that night."
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