It is the question that makes the rest of football's transfer window look like the offerings of a corner shop as it trails the prospect of the father of all epoch-ending mega deals.
But is it really conceivable that Lionel Messi will move himself and an entire one-man culture from Barcelona? Might he indeed walk away from a contract that runs to 2018 and arrive at Stamford Bridge or the Etihad Stadium or that other repository of unbridled wealth, the Parc des Princes, home of Paris Saint-Germain?
The embattled president of Barca says no, it is about as likely as the signing of a non-aggression pact with Real Madrid. But of course he would say that. Anything else would be electoral madness.
There is, though, another instinct which says yes. It is born of the reality that there is evidence, certainly not conclusive but gathering some credence, that the football sorcerer of his age has almost certainly gone past the best of his days.
Of course, this still leaves him on an extraordinary plateau of achievement.
Of course, the best of the rest of Messi is still a dazzling possibility guaranteed to excite the ownership vanities of that famous acquirer of the most expensive modern art, Roman Abramovich - or the desire of Manchester City's Abu Dhabi proprietors to have a firmer sense that their team is now part of the world elite.
The speculation is strong that both Chelsea and City have been sniffing vigorously on the edges of Messi's disaffection with new Barca coach Luis Enrique and his reported angst over the club's lack of wholehearted support in the investigation of his tax affairs.
Why wouldn't they be? Who are better equipped to remain undaunted by a buy-out clause of more than £200m? Who have more to gain by such a uniquely luminous, and maybe inspirational, addition to already formidable squads - and without the risk of disastrous financial consequences?
Chelsea, City and Paris SG can afford the gamble - and maybe, recent developments suggest, there is also something in Messi that puts him in a similar frame of mind.
Something that has never before incubated so quickly in the psyche of big-time football. It is a sense that no team, and no player, not even a Messi, can afford to be seen to be standing still. You move forward or, sooner than later, you may well be lost.
The old Barcelona hand Henk ten Cate, who was head coach Frank Rijkaard's right-hand man when Messi first appeared at the Nou Camp a decade ago, yesterday made one of the more telling contributions to a debate that has, as they say, gone viral since clear signs of a breakdown in the relationship between the great player and the club emerged over the weekend.
Cate advanced the theory that Messi would have flown away from the Nou Camp some time ago but for a promise he made to former coach Tito Vilanova on his death bed early last year. The Dutchman also said: "I think a transfer would be in everyone's best interests. Messi has been at Barcelona quite a while now and he needs a new challenge.
"He's still worth a lot of money but he will only go down from here on. He's been on another level for 10 years. But I'm not sure he will get back to his best. It isn't normal to shine for 10 years like he has done. Most big names can only keep it up for seven or eight years. And to be honest he wasn't at his best last season, even if the statistics were still great."
They are not exactly derelict now. He is in second place in the La Liga scoring table, behind last season's nemesis Cristiano Ronaldo, but the gap is 11 goals and there's not supposed to be such daylight between the world's two most gifted players. The margin is inflated by the Real man's eight penalty conversions, but the reality is that while Ronaldo surges on, exuberantly bestriding the world game, in Messi there is the growing sense of unprecedented doubt about who he is and whether he any longer inhabits a place attuned to his every need.
When Messi missed Monday's open work-out at the little stadium beside the Nou Camp, and disappointed more than 11,000 fans, there was much scepticism over the explanation. Messi reported a stomach upset 24 hours after starting on the bench in San Sebastian, where Barca lost 1-0 to David Moyes' Real Sociedad. Messi's old senior lieutenant Xavi didn't exactly douse the flames with his theory that a stomach upset is one of football's less convincing reasons for a player's absence. "You take a pill and you play," he said.
Nor does it help that Messi was seen arguing with Enrique - another snatch of evidence, along with the spot sacking of director of football, Andoni Zubizarreta, that the Nou Camp story has entered its most rancorous phase in all the years of dynasty.
What is beyond doubt is that the 27-year-old Messi has reached a point in his life when there are questions he has to answer, to himself and a still largely adoring public. He hinted as much earlier in the season when he declared, "Football is full of unexpected twists and turns. It is true I've said I would like to stay at Barcelona forever but sometimes not everything turns out the way you want."
Certainly last summer's World Cup looms high in such a category. One of the most stubborn memories is of a plainly embarrassed Messi behind pushed forward to receive his player of the tournament award.
It was a critical travesty of course, and the look on Messi's face was that of a man who knew that he had traded most profitably not on his most sublime gifts, and consistent relevance to any game, but his reputation.
That has never been Messi's style. If his talent was for so long astonishing, so too was his consistent desire to deliver the best of it. When he failed to do so in the World Cup final against Germany, it felt a little like the breaking of a spell, the end of something that had been promised in the sky.
In Brazil, ever fertile ground for the denial of Argentine genius, there is a belief that Messi is now paying a price for the hormone treatment he received as the brilliant but physically frail boy recruited by Barcelona, that he is considerably older than his years.
That may be a theory of dubious provenance but what isn't so easy to dismiss is the possibility that Lionel Messi, for the first time in his stunning career, may be in need of not just a rest but a change. One thing at least is certain. Only those with the most fabulously lined pockets can even dream of providing the cure.