Sampdoria were also interested in the 17-year-old and the next 72 hours could be crucial to the Reds signing the Netherlands U19 international.
Van den Berg made 15 appearances for PEC Zwolle in the Dutch top flight last season.
He would be Liverpool's first signing of the summer if he joins.
The Reds compare Van den Berg to being at about the same level as Joe Gomez when they signed the defender for £3.5m from Charlton in June 2015.
England international Gomez was a key part of Liverpool's defence last season before injury curtailed his season.