Van Dijk's management company Wasserman Media - who already have strained relations with Southampton after they negotiated the fractious departure of manager Ronald Koeman from Southampton to Everton last summer - issued a statement on Van Dijk's behalf insisting he wanted to be allowed to leave the club after he was fined by Southampton at the start of August.
It is far from certain whether Van Dijk will move to Anfield despite the Dutch defender handing in a transfer request earlier this month.
It seems Chelsea are hoping to use a more discrete tactic in their bid to land van Dijk as the Telegraph say they have made it clear to Southampton they are interested in signing the £60m-rated star but only if they are prepared to sell.
The news comes from Calciomercato.it in Italy, who explain the Dutchman was on his way to St Mary's in order to finalise his transfer to the Premier League side, where he feels he'll get more chances of playing regularly.
Van Dijk took part in training with the club's Under-23s on Monday but is still unavailable for selection. He has not played for Southampton yet this season.
Davis says Brexit trade agreement would progress border issue
It separately raised the idea of a "temporary customs union" with the EU after leaving the bloc. In effect, what they seem to be saying is that they want a customs union tailor-made for them.
Southampton's new Chinese owners have no plans to inject additional capital into the business or to spend money on new players because the takeover was largely financed via a bank loan and contributions from third-party investors.
Van Dijk has not been selected in Southampton's opening two matches, and his future is still up in the air.
Club chairman Ralph Krueger was initially adamant that Van Dijk would not leave during the summer, although all looks set to change if fresh acquisitions in the defensive department emerge.
Southampton have only a few deals in the summer window.
Meanwhile a group of players have left the south coast, including Martin Caceres, Cuco Martina and Jay Rodriguez.
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