The Dutch defender has been public about wanting to leave Anfield this summer after spending last season on-loan at Mainz.
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PSV Eindhoven and VfL Wolfsburg have made attempts for Van den Berg in recent weeks.
However, The Athletic says offers up to £20m have so far been resisted by the Reds.
Instead, Slot and his staff want to take a close look at Van den Berg during preseason, convinced his game has "gone up a level" thanks to his Mainz spell.