Kop boss Jurgen Klopp feared he had lost any chance of landing his man after Saints reported the Anfield club to the Premier League over an illegal approach.
That forced the Reds to end their interest in the player and issue a public apology for their conduct.
It now seems that circumstances have changed and Southampton have a new manager in Mauricio Pellegrino, who insists he will not stand in van Dijk's way.
A large fee is expected to be required in order to sign Van Dijk, who experienced success with Celtic during his time in Scotland, and Brendan Rodgers' side are monitoring the transfer saga closely due to the sell-on clause in the 26-year-old's contract.
Oil prices rise on slower U.S. output growth, strong Chinese demand
The bounce in prices could extend in the near term given that most of the bearish triggers have been baked into prices. Looking ahead, Rs 2,900 is likely to provide immediate support and the short-term bias looks positive above the same.
The classy Dutch star was injured for the second half of last season and at one stage Chelsea looked to have overtaken Liverpool in the race to sign him.
The Daily Express say the French boss is wary of the speculation over Alexis Sanchez's head after he conceded his future may be away from the Emirates.
But with Paris St-Germain and Bayern Munich keen on the 28-year-old, who scored 30 goals for Arsenal last season, a move overseas might yet be sanctioned.
There are likely to be a number of outgoings from Liverpool in the coming days.