Chelsea, Arsenal and Manchester City have also been credited with interest in signing the Dutch defender with the Blues said to have been the frontrunners. Liverpool, however, are hoping Van Dijk's interest in working with the German manager will stand them in good stead as they go head-to-head with their Premier League rivals.
Southampton are reluctant to allow their skipper to leave in the summer and are said to be demanding at least £50m ($64m) if they are to be tempted to part with their prized asset. Van Dijk will become Liverpool's record signing if the deal goes through and he will also equal the record of becoming the most expensive defender currently held by Chelsea defender David Luiz when he moved from Stamford Bridge to Paris Saint-Germain in 2014.
According to the Mirror, Klopp is ready to convince Van Dijk to choose Anfield over other interested suitors with the promise of making him the defensive leader at the club.
The club are also ready to make him one of the highest earners by offering a package worth £200,000-a-week.
The 25-year-old Dutchman has been sidelined with an ankle injury since January, but is still one of the most sought-after players this summer. He has returned to light training recently and it looks likely that he will move in the summer.
Liverpool, meanwhile, are looking to add further depth to their defence and according to the Daily Mail, the Merseyside club are ready to offer Gael Clichy, who has been released by Manchester City a two-year deal to move to Anfield.
The left-back position has been a problem for Klopp after Alberto Moreno failed to meet expectations following his arrival from Sevilla. James Milner was deployed in the left full-back position for most of last season, and the manager is keen to add more depth as they prepare to return to the Champions League after two years.