Van Dijk has been linked with moves to Liverpool, Chelsea and Manchester City but Southampton have insisted he won't be sold this summer.
The Dutchman has become one of the most wanted defenders in the Premier League after two impressive seasons in English football and the Reds are now the front runners to sign the 25-year-old.
No fee has been agreed between Liverpool and Southampton with the Saints wanting around £50million.
But with Van Dijk's preference for Jurgen Klopp and Anfield, Southampton will have to consider whether to keep hold of the player.
Virgil van Dijk's next club: Where could the Southampton star go next? Tue, May 9, 2017
Where could Southampton star Virgil van Dijk go next? Odds provided by 888sport
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Which clubs are tipped to sign Virgil van Dijk? Odds provided by 888sport
Virgil van Dijk wants to join Liverpool
Van Dijk would become the sixth player to leave the south coast for Liverpool since 2014 if he completes the deal.
Adam Lallana, Dejan Lovren, Sadio Mane, Nathaniel Clyne and Rickie Lambert have all moved to Merseyside costing nearly £100m.
Last month Southampton boss Claude Puel said: "He's our captain and I have said he is important for us. He has authority, the leadership of the team, he is a fantastic player.
"It's important for us, of course, to wait until the beginning of the season to see him on the pitch with Southampton.
"He has a long contract and the directors want to keep him."
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