Van Dijk was a top target for the Reds in the summer but no deal went through.
Liverpool were forced into an embarrassing public apology to Southampton after being accused of tapping up the player.
He ended up staying put at St Mary’s but could now be on the move in January.
Irish newspaper the Sunday World report Liverpool have made a major breakthrough in their pursuit of the Dutch defender.
It’s claimed the Kop WILL now sign the 26-year-old in January after a structured payments deal which meets Saints’ £70m valuation was thrashed out in the last week.