It appears the temptation of Champions League football is too much for the Dutchman, who has been linked with a move away since January.
A few weeks ago, it seemed as though van Dijk's Liverpool move was off the table after Southampton accused them of tapping up their centre half.
Jurgen Klopp's club issued an apology to the Saints but are yet to bring in a new central defender to bolster their squad.
And it now appears van Dijk wants to push through a move to Anfield in time for the new season.
Southampton will no doubt be used to Liverpool acquiring their most-prized assets, however, this one will hurt them badly.
New boss Mauricio Pellegrino has admitted he does not want to keep unhappy players at the club, but will struggle to replace van Dijk without spending big money this summer.
In the long run, it also hampers Southampton's progression as a club. The 26-year-old is the latest to decide to up sticks and move to a more attractive club, meaning the Saints continue to remain merely a stepping stone of a club.
Other viable options
Despite Liverpool not making any formal offer for the player, it would seem they are clear favourites to acquire van Dijk's signature.
Chelsea look set to sign Roma's Antonio Rudiger, while Manchester United have already completed a deal for Benfica centre half Victor Lindelof, potentially ruling both clubs out of signing Southampton's main man.
Manchester City were said to also be interested earlier in the window but that particular rumour has went cold recently.