Van Dijk was man of the match last night as the Reds beat Crystal Palace 2-0 at Selhurst Park.
The Reds have kept nine clean sheets in Van Dijk’s 16 Premier League appearances following his move from Southampton.
And Liverpool hero Jamie Carragher says the defender can become an Anfield legend if he continues to impress.
"I knew Van Dijk was a good player, but he is better than what I thought," Carragher told Sky Sports.
Liverpool news: Man Utd tried to sign Virgil van Dijk (Image: GETTY)
"We've always said Liverpool can't win the Premier League because of their defence, but now they have Van Dijk, who I think is the best centre back in the Premier League.
"I can't think of a defender off the top of my head that is better.
"He's the man to step into the position Vincent Kompany has had over the last four seasons as that leader and colossus.
"They are very similar as players - there is nothing they lack.
We use your sign-up to provide content in ways you've consented to and to improve our understanding of you. This may include adverts from us and 3rd parties based on our understanding. You can unsubscribe at any time. Read our Privacy Policy
Liverpool news: Virgil van Dijk was man of the match as the Reds beat Crystal Palace (Image: GETTY)
"When Kompany was at his best three years ago, I didn't think there was a centre-back that was better than him.
"Over the next three or four years, if Liverpool could win a league or a Champions League, I think Van Dijk has the potential to actually go down alongside Alan Hansen if we're talking about Liverpool's best ever teams - that's how good he is and how good he can become.
"If Liverpool under Klopp win something big, and Van Dijk is at the centre of it, he should be disappointed if he's not alongside Hansen when people talk about the great Liverpool centre-backs.
"There isn't another centre-back that ticks almost every boxes in terms of presence, pace, strength and ability on the ball.
Liverpool news: Jurgen Klopp beat Man Utd to Virgil van Dijk (Image: GETTY)
"Normally a player has a couple of those, they are lacking somewhere else and their defensive partner will cover some of those areas. Van Dijk has all of them at the moment.
"Players and leaders like him have to be the ones that take Liverpool to something big.
"That's when you'll be remembered, when you win something big."
Van Dijk and Liverpool are back in action on Saturday evening when the Reds host Brighton in the Premier League’s late kick-off (5:30pm).