The Dutchman was the subject of interest from the Reds in the summer and was keen on moving to Anfield.
However, Southampton blocked a deal after being angered in Liverpool’s approach towards their defender.
Liverpool were forced to publicly apologise after Saints accused them of illegally tapping up their player.
That didn’t put the Reds off trying to close a deal before the deadline though, and Liverpool could renew their interest in January when the transfer window reopens.
But according to the Gambling Times they’ll be disappointed in their pursuit.
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They state Southampton have no interest in ever selling Van Dijk to Liverpool after becoming incensed with their behaviour over the summer.
Southampton sources believe that Van Dijk will remain at the very least for the rest of the season.
Van Dijk has only just returned to the first-team fold under Mauricio Pellegrino after demanding to leave the club.
The 26-year-old made his first appearance of the season earlier this month in their 1-0 win over Crystal Palace after coming on as a substitute.
Despite Van Dijk being under contract with Southampton until 2022, he is still expecting his time on the south coast to be short-lived.
However, with his preferred choice of destination Liverpool seemingly off limits, the defender may have to consider a move elsewhere.
Chelsea and Manchester City both contested the Reds for his signature in the previous transfer window.