The German again goes head-to-head with arguably the greatest coach of his generation in Pep Guardiola, against whom he has a better record than anyone else, having won seven of their 13 encounters.
However, while the Manchester City boss is rightly hailed as a footballing genius, the praise for Klopp can be less forthcoming, with the assumption being the brand of football he plays is less complex, while his over-the-top technical-area antics often detract from a more rounded assessment of his tactics.
Van Dijk, who has only worked with the 50-year-old for just over three months, says there is plenty more the public do not see.
“He is the complete manager. He is a fantastic team manager, player manager as well, and everyone is working hard together,” said the Netherlands captain.
Obviously that [interaction with crowd] stays more in people’s minds, because that is what you see, but he is much more than that. You don’t see all the hard work we put in behind the scenes. He has shown already that he is an outstanding manager.
Van Dijk, the club’s £75m record signing and world’s most expensive defender, will be a key man in their defensive organisation tonight. He has already made a difference since arriving from Southampton in January and insists he can cope with the focus and pressure.
“I’m never nervous. I am just excited. I think: ‘Look where I am. Playing for the semi-finals of the Champions League with my team. Just enjoy it and love it’,” he said.
“I always have been [calm]; sometimes, a little too much. Sometimes, that cost me back in the day, to be fair. Sometimes, you lose, but if you win the feeling is amazing.
“Every game you have to stand up. It is not only this night. I think it is only other people who put pressure on me, but I don’t care really.”
Klopp, meanwhile, maintains it is still only half-time in their quarter-final with City and that should be warning enough for his players.
The greatest moment in the club’s recent history came when they trailed AC Milan by the same 3-0 scoreline in the 2005 final in Istanbul and no-one needs reminding of how that turned out.
However, the last time they led a European match by three goals at half-time was November’s group tie against Sevilla when they conceded three in a crazy 45 minutes to draw.
Should City find a way to reproduce that in the second leg at the Etihad Stadium tonight, there will be all manner of panic within the red ranks, even if Klopp insists they would still be capable of seeing out the game.
However, he will not use the Ramon Sanchez Pizjuan experience as a motivational tool.
“You don’t need to remind them of a specific game,” he said.
I saw the game of City v United at the weekend. It was one of the best first halves I ever saw. It was like a thunderstorm. Then, in the second half, after the first goal, one team gains rhythm, another team loses rhythm. The game changes.
“I cannot tell the boys: ‘Boys! Score early!’ Well, I can, but I am not sure that it really helps.
“We have to think about football: What we have to do, where we have to do it. That’s what I am talking about in terms of not needing examples.
“The boys knew after the [first] game this is half-time. We are in the lead, nothing else.”
Liverpool’s last visit to the Etihad in September ended in 5-0 defeat after Sadio Mane was sent off with the score at 1-0. Klopp maintains much has changed since then.
“It is different. We are longer together. Things are better, but it only shows us that these things are possible,” he said.