Van Dijk moved to Anfield from Southampton for a reported fee of £75 million but was ineligible to feature in Monday's 2-1 win at Burnley in the Premier League.
Asked when Van Dijk would make his first appearance, Klopp replied: "I don't know.
"We made a few tests that make sense only for him and for us, to see where he stands. That's all. There is no rush.
"He is on fire and he really wants it, that's all good, but we have to make sure he can perform.
"Centre-half is a position which depends on all the others on the pitch. There are a few challenges you have to solve by yourself, all the rest is always together. That means you have to tune it so it works really together.
"We need time. A pre-season is for that usually but we don't have a pre-season. Everything will be fine.
"After the Everton game we have a little bit more time, that will help, but it's a long-term project – so it's not important when he makes his first game, it's important how many good games he will play for Liverpool. That's what I'm interested in."