Should the deal go through, Van Dijk could be Liverpool's record signing and the club's highest-paid player ever.
The 25-year-old Netherlands worldwide is fast emerging as one of the Premier League's most in-demand players in the 2017 summer transfer after his commanding performances in the Southampton side.
Van Dijk would be Liverpool's most expensive ever signing - striker Andy Carroll having cost £35 million in moving from Newcastle United in 2011.
But the player's move to Anfield could be overshadowed after Southampton asked the Premier League to investigate whether an illegal approach had been made.
The Southampton defender has always been linked with a move to Anfield ahead of the summer transfer window.
Southampton are set to demand a huge fee should they part ways with Van Dijk this summer, with a fee of £60million thrown around in recent weeks. "Yes", Krueger said, as quoted by the Daily Mail.
The chance to work with Klopp is believed to have been a significant factor in Van Dijk's decision, despite similar opportunities being available with Pep Guardiola and Antonio Conte.
Sky also reported that Van Dijk has been swayed by Klopp's involvement in the potential deal.
Liverpool could have saved themselves the hassle as well as the money if they just signed Van Dijk two years ago.