The Premier League champions were rocked last month when their defensive stalwart underwent surgery on an ACL injury sustained after a rash challenge from Everton goalkeeper Jordan Pickford, with Van Dijk not expected to play again this season.
With Joel Matip also sidelined with a short-term problem, Liverpool have been left light at the back, using youngsters Nathaniel Phillips and Rhys Williams alongside Joe Gomez.
But despite some promising displays from the inexperienced duo, ESPN report that Liverpool are looking to bring in a more proven centre-back when the transfer window reopens.
One of the players at the top of their list is Inter defender Skriniar, who has fallen out of favour under Antonio Conte and very nearly left Italy during the summer window.
Spurs held lengthy talks with Inter over a deal but could not get it over the line in time despite Skriniar being keen to join and were likely to reignite their interest in January even though they signed Joe Rodon from Swansea.
Inter valued Skriniar at €60million (£54m) over the summer, though their bargaining position will be affected if Conte does not restore the Slovakian to the team.
Liverpool have an advantage over Spurs in that they have spent more frugally over the past couple of seasons whereas Tottenham will need to trim their bloated squad and raise funds before launching a bid.
The north Londoners had hoped to return for Skriniar next summer, but Liverpool’s need for a centre-back is far more pressing in the short term.
While Skriniar is seen as reliable cover for Van Dijk right now, he also has all the characteristics needed to play alongside the imposing Dutchman when he eventually returns from injury.