The Netherlands international was ruled out for the majority of the season following a collision with Jordan Pickford against Everton back in October, but he is making good progress.
Van Dijk underwent surgery on his right knee after ACL damage was discovered, which threatened to derail their chances of retaining the Premier League title they won last season.
Klopp has since offered supporters a glimpse into the current situation, with the club recently making a change in their staff to help the defender recover.
Klopp said of Van Dijk: "Good, very good. I have no problem with talking about Virgil van Dijk.
“It’s very good but still a long way to go, that’s this kind of injury.
"I’m happy when I see these videos, to be honest, because it just shows that he makes good progress.
“But it will still take a lot of time, that’s how it is. I would like to say something else but these are the facts, unfortunately.”
That comes after the club sent a physio out to join the 29-year-old at the Nad Al Sheba Sports Complex in Dubai as his rehabilitation continues.
The Reds current sit three points clear of Manchester United in the table at the start of the New Year, but the Red Devils do have a game in hand to come against Aston Villa.
Dutch legend Clarence Seedorf was a guest of Van Dijk in the gym earlier this week, and he said: “I joined the captain Virgil van Dijk for some training today!
“Happy to see his determination and hard work to be back on the pitch stronger than before!
“In these type of journeys, patience and focus are key to succeed. Keep it up my brother!”