The Anfield side have endured a torrid time in season 2014/15 so far and Brendan Rodgers is keen to supplement his squad with new players come January.
Currently sitting 11th in the English Premier League, 18 points behind leaders Chelsea, much of the criticism levelled at Liverpool has been at the lack of goals scored.
But there is also concern at the amount conceded, with speculation that Rodgers could swoop for van Dijk to shore up his back four.
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The Liverpool boss knows that the Dutch centre half would be relatively affordable by Premier League standards, and could put in a bid early in January in an attempt to see off competition from the likes of Arsenal and Spurs.
The 23-year-old has also been linked with Southampton, Sevilla, Hamburg, Newcastle, West Ham and Sunderland in the past few months.
Arsenal were rumoured to be tabling an £8 million swoop in October but Celtic boss Ronny Deila is keen to hang on to the towering centre back.
Van Dijk, who is on the fringes of the Netherlands squad, has played 76 matches in total for Celtic, scoring 11 goals in the process, including a wonderful solo goal against St Johnstone.
He was also part of the defence that went 1,215 minutes without conceding a goal, breaking a 43-year-old record, and won the Celtic Players’ Player of the Year Award.
He was also listed in the 2013-14 PFA Scotland Scottish Premiership team of the year.
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