Liverpool had been heavy favourites to sign the Dutch centre back and the player was reported by British media earlier this week to have told Juergen Klopp's side that he wanted to join them.
The development is the latest twist in a transfer saga involving the sought-after defender who has been linked with a 60 million pounds (77.69 million) move away from St Mary's.
"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," Liverpool said in a statement on the club website.
"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."
Strict rules govern transfers, with clubs able to negotiate terms with players only if they are out of contract or once a fee has been agreed with the seller. The laws also govern indirect approaches via an intermediary.
Southampton have consistently said they do not intend to sell Van Dijk, who joined from Celtic for 13 million pounds in September 2015 and signed a new six-year contract in 2016.
The new deal was a reward for a series of impressive performances at the heart of Saints' defence although he has not played since January after sustaining ankle ligament damage.
Liverpool have regularly plundered Southampton over recent seasons with former Saints players Adam Lallana, Dejan Lovren, Sadio Mane and Nathaniel Clyne all currently playing at Anfield.
Those four players joined Liverpool in deals totalling more than 100 million pounds in the past three years.
The transfer row is the second this year involving Liverpool, who received a two-year ban on signing Academy players from other English clubs after accepting they made an illegal approach for a 12-year-old attached to Stoke City.
Image: Virgil van Dijk
Photograph: Julian Finney/Getty Images
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