The 25-year-old -- who joined Southampton in 2015 after impressing at Scottish champions Celtic -- will cost around £60million (69m euros, $77m), according to reports.
He would also be Liverpool's most expensive ever signing -- striker Andy Carroll having cost £35m in moving from Newcastle in 2011.
Celtic would be in line for 10 percent of the fee having included a sell on clause in the £11.5m transfer to Saints.
David Luiz is presently the most expensive defender in the world having been sold to Paris Saint Germain by Chelsea for £50million in 2014.
According to the "Sun" newspaper, Liverpool manager Jurgen Klopp has convinced the Liverpool owners van Dijk is deserving of earning a weekly wage of almost £200,000 (230,000 euros, $258,000) -- which will make him their highest ever paid player.
Van Dijk -- who also caught the eye of both Manchester City and champions Chelsea -- is keen on a move to Liverpool not only for Champions League football but to join compatriot and close friend Georginio Wijnaldum.
Southampton have become a favoured hunting ground for Liverpool in the past three years having signed five players -- including Adam Lallana and Senegalese star Sadio Mane -- for a total of almost £100million.