The Lille defender will come up against the Reds' skipper at Wembley on Wednesday as Denmark face England at the national stadium.
And for Kjaer, the game might be that little bit more special, with the 24-year-old's dad - as well as the rest of his family - being Liverpool supporters.
As such, they have given him a mission: to bring Gerrard's shirt home with him at all costs.
“My father and the rest of my family are huge Liverpool supporters and my father has literally forced me to ask for Steven Gerrard’s jersey after the game," Kjaer is quoted as saying by Daily Mirror.
“So I am a man with a mission - also after the game. For the first time in my career I have to go to another player and ask for his shirt - and that’s a bit embarrassing, really.
“I have never done that before, because normally you just exchange jerseys with the guy you play directly against."
For his part, Kjaer is also a big admirer of the England captain.
That's why the 24-year-old will be relishing facing the Three Lions on their own turf, even though Denmark have no World Cup finals to prepare for this year, having failed to qualify.
“I’m pretty much down to earth with full focus on football and not easy to impress - a player and not a fan," the defender said.
“But I must say that Steven Gerrard is a very special character and player who deserves the highest respect from anyone in the world of football.
“The England game is a great test for us against a big football nation even though sadly for us not a test before the World Cup."
image: © nathan17