The Norway midfielder was linked with the Reds going into the tie.
And at the final whistle, Klopp made a beeline for Berge to embrace him and offer some encouraging words.
VG reports Klopp told the youngster, "You are an interesting player, a very interesting player".
Asked about the chat, Berge later stated: "It was a great moment. It is nice. You take it with a smart smile. It is nice that such a reputable coach comes away and says something like that.
"But overall, it's the team performance I'm happy with. We pushed ahead, got up and playws evenly with Liverpool throughout the match. That's what matters most."