Reports earlier in the week claimed the Saints were threatening action over the Reds's pursuit of their player as they felt an illegal approach had been made.
It was claimed the Netherlands international had told Liverpool he wanted to join them without the clubs having opened negotiations regarding any transfer.
In a statement on their website, Liverpool apologised for any misunderstanding and confirmed they would no longer look to sign Van Dijk this summer.
"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," it 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."
Van Dijk has been the subject of intense transfer speculation for a number of months after impressing for Southampton since his arrival in the summer of 2015.
Chelsea have been following his progress while he remains on Manchester City's radar, though a big money move for Monaco forward Kylian Mbappe could put any move to the Etihad Stadium on hold for the time being.