Sheen, who will be 42 by then, described the prospect as "a dark spectre rolling over his future." More like a dark ghost from his past; he should have played the role ten years ago.
Indeed, at the time of his Caligula at the Donmar Warehouse, he told me he was going to do the role with Michael Grandage at the Donmar, but Grandage then suddenly fell in with Jude Law - who himself might have been expected to play Hamlet at the Young Vic, the theatre he is most associated with.
Still, Sheen will be worth the wait, I'm sure; I bet he'll be the most electrifying prince since Jonathan Pryce."It's the most dangerous play in the Western canon," he said, "so I hope I'll have the courage to go to its dark heart."
Pryce turned up, intriguingly, on Sheen's programme, revealing that the demonic and tormented nature of his performance was partly due to the idea of unfinished business with his father, who had been attacked in his own grocer's shop, and had subsequently died.
It wasn't mentioned, but Simon Russell Beale's Hamlet was similarly, perhaps less pertinently, flooded with grief at the recent death of his mother.
Sheen's programme compiled recorded extracts from a harvest of Hamlets from Beerbohm Tree in 1908 to David Tennant in 2008, including snippets of Forbes Robertson ("a voice dipped in Horlicks"), Gielgud, Olivier and Branagh.
A professor at Warwick University, Paul Prescott, argued that the first overtly Oedipal Hamlet was not Olivier's in 1937, as commonly thought, but John Barrymore's in 1922. And there was fascinating testimony from Frances de la Tour on her brilliant, angry, swaggering Hamlet at the Half Moon in 1979, and Michael Billington on Angela Winkler, to explain the female appropriation: "There's not another part to match it," said de la Tour, simply.
Rory Kinnear said he'd been less anxious about the role than Sheen appears to be: "You have to be rigorous about pursuing a clean slate." He hadn't felt hampered by the ghosts of the past, but liberated by them.
No-one seems too fussed about the impending Arts Council cuts, either, except for Colin Tweedie of Arts and Business, who blustered unconvincingly on the lunchtime news about being targeted.
He's no doubt doubly angry because Nick Starr, the NT's executive director, who never speaks up all that often, suggested that Arts and Business should be fingered for cuts some weeks ago.
There was a time when Tweedie's organisation did sterling work in helping subsidised companies find sympathetic philanthropy in the commercial sector.
But every theatre has its own development officer these days - hell, Hampstead Theatre even has Libby Purves's American niece rattling the collection box - and the anomaly of the Arts Council funding an organisation to raise money looks odder by the day.
The arts world knows what's coming to it - as we all do - and has quite a long time now to prepare for the Arts Council's imposed accumulative loss of £100m over the next four years. As Hamlet says, the readiness is all.