The Reds paid £75 million - a world-record fee for a defender - to sign Van Dijk from Southampton earlier this month to strengthen their much-criticised back-line.
Liverpool have found more consistency since then and are two points better off than Tottenham ahead of Sunday's meeting at Anfield, but Klopp acknowledges the magnitude of the test his side face against their fellow top-four chasers.
"He is a big and tall player, that is how it is".
"We have the best nutritioning department and nobody came to me and said to me that we need to work with him".
Danny Ings has also been rewarded for some lively cameos with a place in the squad, with the striker recovering admirably from back-to-back cruciate ligament injuries.
Van Dijk is likely to replace Dejan Lovren, who was substituted after 31 minutes at Wembley having endured a torrid time against Harry Kane, even if Klopp accepts the Dutchman is still getting to grips with his methods. "It's more hard when you've lost two games but you need to be serious still". That is why they played and Virgil didn't play. "But we need really the right thing".
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"I spoke to him and he expected it".
"We had a lot of talks already", he continued, noting that it is "quite difficult" for Van Dijk to adjust to Liverpool's "defending style" because of how drastically different it is to Southampton's style, or that of the Netherlands national team's.
Jamie Carragher and Gary Neville have both questioned some of the decisions taken by Liverpool during the January window, with Philippe Coutinho and Daniel Sturridge both departing, despite no reinforcements arriving to strengthen their forward line.
"Would we have preferred to keep Phil Coutinho? He is a great player but he does not play in a position for which we urgently need new players".
"I'm very happy with Virgil", he added. It's clear, in half a year, Virgil will be a completely different player to last week or next week.