The Saints had reported the Merseyside club to the Premier League over an alleged illegal approach for the defender. It was claimed that Liverpool had contacted the player directly without having agreed a deal with his current employers.
Van Dijk has been part of a tug-of-war between Liverpool, Chelsea and Manchester City, who are all keen to sign him this summer. The Reds were reportedly leading the race to sign the £60m ($78m) rated defender owing to his affinity to play under Jurgen Klopp.
Southampton had made it clear that they have no interest in allowing the Dutch defender, who signed a new six-year deal just last year, to leave the club this summer. Despite their attempts to subdue talks of his potential exit, it was believed that Van Dijk will move to Anfield to become the German manager's first summer signing, which led to an ultimatum from the south coast club and it has forced Liverpool to end their interest and offer a public apology.
"Liverpool Football Club would like to put on record our regret over recent media speculation regarding Southampton Football Club and player transfers between the two clubs," a statement on the club's official site read.
"We apologise to the owner, board of directors and fans of Southampton for any misunderstanding regarding Virgil van Dijk.
"We respect Southampton's position and can confirm we have ended any interest in the player," the statement added.
'De Vrij approach'
Klopp remains keen to sign a central defender this summer and according to Sky Italia, the German manager has already turned his attention to yet another Dutchman in Stefan de Vrij.
According to Football Italia, Lazio have rejected Liverpool's first offer of €20m (£17.3m) for the centre-back, who is out of contract next summer. De Vrij has rejected an offer for a new deal from the Serie A club fueling talks about a summer move.
Chelsea and Inter Milan have also reportedly enquired about the availability of the defender, which has prompted the Merseyside club to step up their pursuit with an initial bid. However, Lazio, who are said to be willing to sanction a sale value the player at €35m.