Virgil van Dijk has told Liverpool he wants to join them over Manchester City, Chelsea and Arsenal, according to Sky Sports.
The report suggests personal terms between the clubs have not been agreed.
But Liverpool is willing to match Manchester City's recent offer of £200,000-per-week.
Southampton is holding out for a £60m fee, and it is believed Liverpool have come to terms with paying nearly double their club record for the Dutchmen.
Bookmaker Ladbrokes has suspended all betting on the transfer as Jurgen Klopp closes in on his second signing of the summer after Dominic Solanke recently agreed on a move from Chelsea.