Van Dijk is expected to miss the majority of the rest of the season having been injured by Jordan Pickford in last weekend’s Merseyside derby.
The Dutch defender is set to undergo surgery on his ACL with many players missing large chunks with similar injuries.
Return date targets are common with managers often providing updates on when their star players hope to be fit again.
But, in somewhat unusual circumstances, Klopp insists he doesn’t want to know how long he will have to cope without Van Dijk.
Klopp said: “Virgil was here, he’s OK. But about when the surgery will happen and stuff like this, I don’t think it makes sense that we give pretty much a time schedule every day.
“But it will be fine and will happen in an appropriate time. So, that’s it pretty much – he is as good as possible.
“We don’t even want to know it [timescale], to be honest. It will take time, that’s clear.
“In the end, it’s really like this: all people are different and so we should not limit that by saying ‘for him it was that long, for him it was that long’.
“I think it makes sense from a specific moment in the recovery, in the rehab time, that it becomes individual because then everybody copes differently with it and each body. That’s why [there is] no need for [a timeframe].”
The Athletic’s David Ornstein had worried Liverpool fans, explaining that the injury could be worst than expected.
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He said: "It's my understanding - it's not official - that the damage to Virgil Van Dijk's right knee is perhaps worse than initially feared and could extend beyond the ACL.
"It's unfair to speculate further or give further detail but... it would indicate that we won't see Van Dijk back on a pitch until next season.
"He will now undergo surgery. Exactly when, we don't know."