Firstly, the hard man with a wealth of football experience. Secondly, the big name. Thirdly, the "Irish narrative", for want of a better phrase. Fourthly, the implacable (if complicated) disciplinarian.
Keane is all of these and more. The only thing missing from the arguments to make him the next manager of Celtic is his record in this particular line of work. At best, it is erratic. At worst, it is unimpressive.
The 42-year-old is hanging around in a distinctly bit-part role as assistant to Martin O'Neill, the Republic of Ireland manager. This is not a job many believe Keane wants to have for any length of time. What he craves - whether it be at Celtic or elsewhere - is another crack at being a No.1.
So there seems a happy coming together of circumstances here, what with Dermot Desmond, Celtic's majority shareholder, said to be keen to appoint him, and Keane himself also in a mood to be a manager once more.
Whether Peter Lawwell, the Celtic ceo, sees it all quite in this light is a moot point. Lawwell cannot possibly buy all the guff about Keane "putting bums on seats" at Parkhead merely through being Roy Keane - it will require a lot more than that. Lawwell may also take a more forensic look at Keane's record as a football manager and reach a different conclusion about his readiness for Celtic.
Keane's record as a manager is a peculiar mix of stellar success and abysmal failure - with the emphasis more weighted to the latter. In his five seasons in English football he inspired Sunderland and Ipswich to the following positions: one title and a series of relegation battles.
Were Keane anyone else, given this rate of regress, he wouldn't even be mentioned today for a major job in football.
So it must be other stuff that makes Roy Keane's name a contender for such positions as the Celtic manager. His reputation as a footballer, despite hanging up his boots seven years ago, appears to remain a factor. Then there is his reputation as the icy assassin of TV punditry. In truth, Keane appears to thrive on aspects that give him a fame or an infamy, but which seem way down the list of criteria by which you would judge a prospective new manager. Specifically, in this context, he has been found wanting.
The key here, naturally, is his relationship with Desmond. The businessman can call on Keane at any point, and recognises his force of personality, and appears very keen to bring him to Celtic. In a sense this may be all that matters. What Desmond wants - right or wrong - he normally gets.
Football remains a random, unpredictable business. If he does become the next Celtic manager, there is the possibility that Keane could make a success of it. Unless he proves utterly incompetent, he should certainly stockpile some domestic trophies. The real test, given this, is what nous Keane could bring to Celtic in two further spheres. First, in terms of building a new team. Second, in terms of his ability in the Champions League.
Mention of European football and Roy Keane raises another weird aspect - which is that, as a manager, he has no experience of it whatsoever. Again, this might not mean much: perhaps he could prove himself masterful in that environment. But the simple fact is, as a coach, Keane has never been there before, to breathe his ire over the occasion.
Some flawed comparisons have been made between Keane and Neil Lennon, usually from those who are promoting Keane's case for Celtic. The crux of their case is that Lennon was an untried manager when appointed in 2010, who also represented a "risk" to Celtic.
This isn't quite true. Firstly, Lennon did some coaching at both Nottingham Forest and Wycombe Wanderers in 2007. He then returned to Celtic in 2008 to become Gordon Strachan's first-team coach. For nine months Lennon then became the manager of what was, in effect, Celtic's reserve side.
In March 2010, following Tony Mowbray's sacking, Lennon was put on trial as Celtic caretaker manager, and given eight league games in which to prove himself - and won all of them. Throughout this period Lennon as a coach suffered none of the medium-term failures which Keane unfortunately stockpiled for himself following his first successful season with Sunderland in 2006-07.
In this whole debate about Keane and Celtic, there is no doubting who would love the appointment the most - the Scottish media. Unless Keane has suddenly mellowed and softened with age - which I doubt - you could almost start writing the headlines now in advance. The dramas, rows and rumpuses would be guaranteed. Keane at Celtic would be tremendous fayre for the newspaper business.
More wary Celtic supporters will be less concerned with this than with Keane's track-record for getting the job done. It is, in short, an uninspiring citation.
As much as Sunderland fans still adore Keane for what he gave them back in 2007, many more fans across Britain have watched Keane's unsuccessful sabre-rattling in the game since then. Little wonder that Sir Alex Ferguson quickly backed off from his original notion that Keane would be a success in the dugout.
I don't know if Keane could be a successful Celtic manager or not - perhaps he could be. But, on the available evidence, he will be lucky to get the chance.