Only three players in the Premier League have the ability, when at their awesome best, to make everyone else on the pitch look like immature creatures, toddlers trying and failing to compete with giants. Two of those players are on the wane – Yaya Touré and Zlatan Ibrahimovic – but the other should be approaching his prime. If Liverpool sign Virgil van Dijk they will be making the ultimate upgrade to their team.

On one level it could be argued that to splurge £60m or thereabouts on any player is to blare a huge scouting or coaching failure, since a really savvy club might be able find or develop a less obvious solution. But in terms of forking out for a surefire success, there is no better signing than Van Dijk that Jürgen Klopp could make to improve his rickety defence, no single purchase that could demonstrate more clearly Liverpool’s determination to clamber back atop that long-vacated perch.

Doubts about the seriousness of that ambition gained traction recently as the club’s apparent willingness to make do with half-cocked solutions suggested that their American owners might be satisfied with becoming the new Arsenal, full of tempered hope rather than true-blooded conviction. Signing Van Dijk would dispel such a notion. Of course if Van Dijk really has set his heart on a move to Anfield, then failing to complete the deal now, especially due to gauche antagonisation of the potential seller, would make the new Arsenal tag so apt that Liverpool might as well bang a cannon on their crest.

Van Dijk was majestic at Celtic and has been regal at Southampton, where, as soon as he arrived two years ago, he assumed a lordly guise, healing everyone who pined for Toby Alderweireld. Powerful, fast and perceptive, he dominates in the air and on the ground, often with seemingly effortless grace. Simon Mignolet and Liverpool’s defenders have seemed locked into the opposite of a symbiotic relationship, a mutually debilitating bind in which the flaws of each sap the confidence of the other and ensnare the lot of them in a vicious circle of decrepitude. Van Dijk is commanding enough to break that chain and impose order and confidence. That does not mean, of course, that Liverpool would not benefit from enriching their squad with a goalkeeper and left-back as solid as Fraser Forster and Ryan Bertrand respectively, but Van Dijk’s arrival would make such additions less urgent.

Liverpool badly need a wholesome meat-and-potatoes centre-back, a stalwart who excels at defending’s fundamentals. Picture Mamadou Sakho on a good day. Now picture Sakho having a good day nearly every day. But Van Dijk is much more than that. He is that most precious of talents, a ball-playing centre-back of the sort that John Stones can supposedly become, a stopper who also creates. He can sashay forward with even more finesse than Joël Matip and, to boot, is a potent aerial threat from set pieces and can even take a mean free-kick. Whether in a back three or a back four, he could be Liverpool’s answer to David Luiz, and more.

If Van Dijk is sincere about wanting to join Liverpool despite more lucrative offers from elsewhere, that speaks well of his character and that of Klopp. It suggests that he distinguishes between merely winning and winning gloriously, being a champion and a hero. At Liverpool his aim would be to become a leader in the team who satisfy one of English football’s most intense cravings, that generation-long yearning for the restoration of their domestic crown, and maybe their European one too. Nothing he could achieve at Chelsea or Manchester City could beat that.

If Southampton were to be seen to sell Van Dijk without a fight, meanwhile, then that, on the back of so many other sales, would confirm that they have different ambitions. To be acclaimed as canny scouts and developers would appear to be enough for them, and would make them, in one sense, a definitive success story of the Premier League age: expert and very well-paid middle men.