Liverpool have plundered St Mary's over recent seasons, with Adam Lallana, Rickie Lambert, Dejan Lovren and Nathaniel Clyne all heading to Anfield.
And the London Evening Standard claim Liverpool are once again gearing up to sign another of Saints' best players.
According to the report, Liverpool are aware that Southampton will demand at least £50m for Van Dijk - the fee Manchester City paid Everton for John Stones last summer.
And Reds manager Jurgen Klopp highly rates the centre-back.
Chelsea pushed hard to sign Van Dijk last summer but Southampton held firm on their reluctance to sell.