There was a stir in the art world a few years back when the great “lost” American painter Nat Tate was dramatically rediscovered. Tate, the story goes, was a member of the New York scene of the 1950s, who ended up jumping to his death off the Staten Island ferry after visiting Europe and finding himself haunted by the genius of Braque and Picasso. The Tate retrospective opened in London with a speech by David Bowie and a tribute from Gore Vidal, who knew everybody, so naturally knew Tate too. Critics at the launch nodded sagely. Tate was obscure – they knew the name, of course – but perhaps it really was time for a re-evaluation of this strangely overlooked contemporary of Jackson Pollock and the mid-century greats who ... well ... didn’t actually exist.

Tate, it soon emerged, was an amusing cut and paste hoax by the novelist William Boyd, in part inspired by his irritation with the hype over the “Young British Artists” of the times, many of whom were, as Boyd later noted, “not very good”.

The reason for mentioning him here is simply that Tate sometimes pops into my head whenever the cultishly revered, relentlessly name-checked Argentinian football coach Marcelo Bielsa is mentioned in some unlikely passing context, as he was this week with the republishing of a leaked shortlist of candidates to replace Sam Allardyce at West Ham.

You can imagine the talk around the boardroom table on this one. OK, so who have we got then? Respected club legend? Slaven Bilic. Tick. Premier League veteran? Rafa Benítez. Got it. Right, all we’re missing now is an eccentric idealist who values academic process above winning and who once wandered around for several days wearing a pair of shoes on which he’d drawn an outline of feet to illustrate some fine point of technique to his players.

Bielsa to West Ham: it’s a compelling prospect. But then he’s a compelling kind of guy, a seductive and in many ways very funny giant of the modern game. Certainly if Bielsa didn’t exist it would probably be necessary to invent him, and there is no doubt his legend has been allowed to develop a slightly exaggerated, cartoonish edge: the manager as crackpot chess genius, nerd god, wandering the streets in his carpet slippers in search of some fleeting glimpse of the footballing absolute.

“There are 36 different forms of communicating through a pass,” Bielsa once said, and you can already feel yourself nodding. Yes! More! So much so it is even possible to imagine, here in landlocked Premier League-land, Bielsa himself could turn out to be an elaborate hoax, an in-joke concocted by South American intellectuals at the expense of lonesome English tactical romantics everywhere.

Except, of course, unlike Nat Tate, Bielsa is real and currently working in France. This week, as the West Ham link flickered in the background, a video emerged of him addressing his Marseille team after their 0-0 draw with Lyon last month. It shows Bielsa giving a beautiful, slightly maniacal speech about collectivism and team endeavour that drew applause from his players and provides above all a reminder of his allure, the sense of someone oddly untouched and otherworldly, concerned solely with method and form.

And what methods they are. At Athletic Bilbao Bielsa produced an array of impenetrable diagrams, cool green Rothko squares decorated with gloops of colour, angry squiggles, cartoon hieroglyphs illustrating how his player should always be in motion. “Running is understanding, running is everything,” he has said, and his teams do run, pushing forward always – defence is simply the first stage of attack – and resembling at times a kind of wired, luminous, footballing modern jazz.

In this sense Bielsa isn’t Jack Kerouac, the star turn, the headline act. He is instead the Neal Cassady of modern football: the pure idealist, the guy who inspired the guys, and from whom so many managers have borrowed a little, from the more diffuse to to outright acolytes such as Pep Guardiola or Chile manager Jorge Sampaoli, who used to listen to Bielsa speeches on a walkman while he went out jogging.

So: West Ham then. It probably won’t happen. But wouldn’t it be great? Firstly for that rare thing, a genuine clash of cultures: football’s great professorial puritan at work in its most cheerfully philistine league. Bielsa is a guaranteed provocation for those who like to see English football as an unmasker of artifice and pretension, and in which even Louis van Gaal – who could, frankly, dine out for ever just on that transformative Ajax team of the mid-1990s – was being fitted up earlier this season as another empty professor, another Josef Venglos, another Nat Tate.

In which case wait until they get a load of Bielsa, whose reputation as a modern great rests on intangible moments of tactical innovation, who doesn’t win trophies and whose teams have often enjoyed intoxicating peaks matched with sudden dips, in part because he appears at times to be asking his players to do something impossible, to sustain some personal vision of sublime unceasing movement.

Bielsa to West Ham remains an unlikely dream. But take a step back and there is a case to be made here. West Ham’s fans demand attacking, progressive football, which is pretty much all Bielsa is interested in. The current owners seem to want a long-term plan and Bielsa is all about plans. This is a club that has traditionally allowed its mangers to settle and which also isn’t afraid of a certain academic intensity, from Malcolm Allison and the Cafe Cassettari set, with their tactical arguments over the squeeze ketchup bottle; to Ron Greenwood – in his own way a kind of homespun proto-Bielsa, – the tracksuit obsessive with his Hungarian fixation, his endless hours on the training pitch before eventually being dragged off in a daze still muttering about plans and formulae.

Above all it would simply be great fun and a deliciously counter-intuitive move for the league that doesn’t think, the league that likes instead to bump along in a state of profitable stasis. And which is perhaps missing a little intellectual content to go with the generalised excitement, a different kind of passion beyond the familiar operetta.