Nagelsmann became the youngest head coach in Bundesliga history when he was appointed at the age of 28 in October 2015 and has won admirers across the country for his work over the last two years.
Klopp hailed Nagelsmann as a shining example of Germany's promising coaching talent and expects a difficult task when Liverpool face Hoffenheim in the first leg of their Champions League play-off on Tuesday.
"I'm really happy for my friend and agent because I'm the old horse in the stable and there's a young horse already!" Klopp told a news conference.
"He's a big, big coaching talent. We don't know each other very well but I've followed his way because I like good football.
"He's not the only one but he's a good example of a lot of really good young managers in Germany.
"We're looking forward to the game, knowing about the quality of the opponent. It's just good to be here and have the chance, even when you know it's really hard.
"They are strong, we are strong. That's how it should be."
Liverpool last played a Champions League match against Basel in the group stage of the 2014-15 season but the five-time European champions are the favourites to progress from the tie.
Klopp, however, does not believe his side's level of experience compared to Hoffenheim's will be an advantage.
"I'm not really interested in the experience an opponent has," he said. "We've been together for 20 months, I think, we always try to give good analysis for our players.
"We show them images of the opponent and they speak for themselves. We have an opponent who are very strong, aggressive, who use tactical fouls. We know about their quality and what they do on the pitch and we know it will be difficult like it always is in the Champions League."