Stories circulate about his womanising (compulsive), about the size of his penis (generous) and about his love- making skills (fabulous). He also possesses the holy grail of masculine attractiveness: rugged physical presence combined with gentleness and sensitivity. He is 6ft 4in and a former boxer, but with soulful eyes that make him seem as if he's in deep, existential pain.
Still, Hollywood is full of good-looking Irish actors trying to make it into the big-time. Most of them are struggling. Patrick Bergin has not had a hit for three years, since playing Julia Roberts's psychotic husband in Sleeping With The Enemy. Pierce Brosnan disappeared into camp hunkiness in the glossy supersoap Remington Steele - a role he sent up in last year's Mrs Doubtfire. Gabriel Byrne seems to have given up acting in favour of producing, notably In The Name of the Father.
Liam Neeson stuck it out. He spent seven dogged years in Los Angeles, living out of suitcases, doing big-budget flops (Shining Through), small-budget flops (Under Suspicion), playing third male lead in modest successes (Woody Allen's Husbands and Wives). Not even Neeson bothered to defend some of his films. 'I felt sick to be associated with it,' he said of the ultra-violent The Dead Pool, in which he played a porn film director. 'An awful movie,' he admitted after a turn as an ageing rock star in Satisfaction.
Stress, rejection and fear led to a stomach abscess, and in 1988 he had to have part of his colon removed. The only thing that seemed to be going well was, as always, his love life: having left Helen Mirren behind in London, he went in for serial celebrity dating, from Julia Roberts and Brooke Shields to Barbra Streisand.
But last year, against all odds, Neeson broke through - ironically when he returned to his roots on stage. He began his acting career (after dropping out of teacher-training college), with the Lyric Players Theatre in Belfast and then the Abbey Theatre in Dublin.
His performance on Broadway in Eugene O'Neill's Anna Christie became the hot ticket to Hollywood. Celebrities clamoured to pay their respects, including Francis Ford Coppola, Paul Newman, Gregory Peck and Steven Spielberg, who promptly cast Neeson as the lead in Schindler's List.
The film earned him ecstatic reviews, covers of numerous American glossy magazines, and an Oscar nomination. William Hill is offering odds of 9-2 on Neeson winning the award for best actor, to be announced on 21 March. His next role, in a drama called Nell, is opposite Hollywood golden girl Jodie Foster, and starts shooting this spring. Conveniently, the film also features his current inamorata, Natasha Richardson, who co-starred with Neeson in Anna Christie and who is currently in the process of divorcing the producer Robert Fox. The year's only downer? A severe case of piles.
So how did Liam Neeson - a working-class Catholic boy from Northern Ireland, with wonky teeth and a broken nose - manage it?
There are two theories, the first being simply that talent will out. 'There are actors who want to be stars,' says David Leland, who directed The Big Man, 'and there are those that want to be actors. Liam is one of the latter. Actors who want to work in movies have to live in LA - think of Gary Oldman or Tim Roth. But Liam never lived a starry life, cultivating the Hollywood social scene. I often stayed with him, and he would stay at home and read scripts, watch television and keep fit.'
Don Macpherson, who wrote The Big Man, concurs. 'People who want to be stars are much more ruthless than Liam. They would never take on such projects as The Big Man or Ethan Frome (adapted from the Edith Wharton novel). People who want to be stars are far more skilful at manipulating their public image. Liam has never exploited his good looks. He is simply an actor who has always had star potential.'
The second theory is that Leeson has a ruthless determination to make it, whatever the cost. After interviewing him in 1990 for the London listings magazine Time Out, film critic Geoff Andrew wrote, 'few actors I've encountered seem as consciously motivated as Neeson'.
'I've done a hell of a lot of films in the past few years,' said the actor in that interview, 'and some of them weren't as good, but that doesn't matter so much because I did it partly to get my face known. It was very deliberate . . . even if it doesn't turn out too well, at least I'm getting practice in front of the camera.'
Neeson's love life appears to be part of his game plan. 'I've never had marriage and families and stuff, so I don't miss it,' he said recently. 'I operate better on my own - that's the only way I feel I can work . . . a family would be an added responsibility. It's easy to pack a suitcase and go off to do a film or a stage play and not have to think about a wife and children.'
Indeed, David Leland's claim that Neeson remains resolutely uninterested in the celebrity social scene is hard to square with his high-profile romantic attachments. To be sure, Julia Roberts was an unknown when he met her on the set of Satisfaction. But Neeson himself credits Helen Mirren, with whom he lived in the mid-Eighties, with providing an entree into London's theatrical inner circles.
And Natasha Richardson, of course, happens to be part of one of the world's most powerful acting dynasties. It was she who invited David Leveaux to direct her in Anna Christie, and who wanted Neeson as her co-star. Leveaux will be directing the couple again this year in Strindberg's Miss Julie in New York - where Neeson has now bought an apartment. Later, the trio hope to collaborate on a film of Therese Raquin. Neeson and Richardson look set to become the Ken - another working-class lad from Northern Ireland - and Emma of the mid-Nineties.
Neeson's success, though, is due in no small part to his personality. 'He's incredibly charming,' says Stephen Woolley, who produced The Big Man and the Irish comedy-cum-ghost story High Spirits (one of Neeson's medium- budget flops). 'I fell for his charm. Most people - male or female - fall for Liam's charm. He's very gentle, very polite, not pushy, genial. He's thoughtful, intelligent, never embarrasses himself on set - in every way a pleasant person to work with.'
And of course there's the sex thing. 'I am big, I am a physical actor, and I can appear tough,' he has said, 'but I can also be tender and I hate violence.' Leveaux describes this quality - evident in Anna Christie - as 'innocence and enormous masculine sex appeal'.
Neeson seems to possess - like Sam Shepard - the inner loneliness that women often find irresistible. I'm the one, they fondly believe, that can heal his pain. Yet according to Mirren, whom he met on the set of his first film, John Boorman's Excalibur: 'He doesn't need women. They need him, and he's very graceful with that fact . . . (but) there's a side to Liam that is a real loner. There's a part that no one will ever penetrate.'
This quality is part of Neeson's great skill as a film actor. 'He has an introversion which reads on film,' says Leland. 'Ken Branagh is all peripheral action. Liam can be heroic without losing depth.'
Neeson's hunkiness is also, of course, crucial to his screen persona. In Hollywood, at least until Schindler's List, this may have limited his acting choices. 'He's charming and good-looking,' explains Leveaux, 'so everyone in Hollywood assumed he was a male bimbo. Actresses regularly experience this. But after Anna Christie, suddenly people sat up and realised he could act, too. He has great range. He can get to the end of a sentence without running out of breath. He's also Irish, so he knows about language - it's second nature to him. His performance was incredibly sophisticated and bold.'
So is the coronation of Liam Neeson merely a by-product of America's infatuation with British and Irish culture? After all, his fellow Oscar nominees include Sir Anthony Hopkins, for his performance in Shadowlands and In the Remains of the Day, and Daniel Day- Lewis, star of In the Name of the Father.
The answer is that Neeson's achievement represents a clear shift. Until recently, Hollywood has liked actors from the other side of the Atlantic to be posh. Daniel Day-Lewis broke through as a character actor, in Merchant Ivory's A Room with a View - a film which celebrated the green and pleasant version of Britain. The fact that he was the son of a poet laureate also helped to create the right mystique.
Neeson's success is a class breakthrough. 'Liam's roles and persona are working-class,' said Woolley. 'You could hardly cast him in Shadowlands and In the Remains of the Day, as an archetypal English gent.' Yet he has been embraced, hulking physicality and all, by Hollywood - the first from this side of the pond to have done so for years.
Woolley thinks Neeson will win the Oscar. Leland hopes he won't. 'They say once you've won an Oscar you won't work for two years,' says Leland. 'You can get pigeon-holed. How many roles are there for womanising German industrialists?'
Whatever happens at the Oscars, Neeson is finally - at the age of 42 - on the Hollywood A-list. An equally intriguing question is will he or won't he marry Natasha Richardson?
The signs are good. According to Leveaux: 'Liam has a phenomenal capacity for love.' While Leeson once has said, 'Generally speaking, I think women come into their own in their late twenties, whereas men don't seem to get their act together until their early forties.' Richardson is beautiful and brilliant and 29 years old.
William Hill, however, is not offering odds.