However, as anyone who has ever met the former Ireland ful-back and now Harlequins director of rugby would tell you, O'Shea is hopelessly unsuited to any such role. For one thing, he is honest. For another, he is open and friendly. Finally, when it comes to rugby he clearly knows what he is talking about.
Which is why, after all the posturing, the pettiness and the megaphone diplomacy that has surrounded the matter of a new settlement for European rugby competitions in recent weeks, it was a pleasure to hear O'Shea hold forth on the subject at Kingston Park the other day. Obviously, O'Shea has Harlequins' best interests at heart, but his measured and dispassionate assessment of the issues at stake was a refreshing contrast to the selfish tub-thumping that has characterised most of the debate.
Not that many in the English game have a tub to thump at the moment. Last week, when the French clubs threw in their lot with the Celts and Italians by confirming their involvement in next season's Heineken Cup, the move appeared to leave English clubs isolated, not-so-proud owners of the breakaway Rugby Champions Cup competition in which they will now be the only participants. The situation for future seasons is still unclear, but the short-term reality is that the English sides, having been so bullish on the matter beforehand, have an awful lot of egg on their faces.
As things stand today, the English will not be involved in next season's Heineken Cup. That situation may change within the next few days as further discussions go on, but the English are not exactly negotiating from a position of strength. Caught between the rock of their abandonment by the French sides and the hard place that is their commitment to the television deal they signed with BT Sport last year, there is only limited scope for compromise. If they are involved in Heineken rugby in 2014-15 then they had better learn how to play with tails between their legs.
That, at least, has been the response of the Celts. And as the English clubs, represented by their umbrella group Premier Rugby Limited, had been less than gracious when they thought they held all the cards, such schadenfreude is understandable. But not exactly productive.
The fact of the matter is that a European competition without English involvement is not a European competition at all. It has a huge asterisk against it. I have massive admiration for Ulster's feat of winning the cup in season 1998-99, but it would be a denial of the obvious to say their triumph was not tarnished by the fact no English teams took part that year. England, building towards the World Cup win in 2003, was the powerhouse of European rugby at the time. Bath had won the cup the season before Ulster's victory; English sides would lift the trophy in each of the three seasons that followed.
O'Shea's Harlequins have not exactly set the European heather alight through their participation in the Heineken Cup, never getting past the quarter-final stage. And having lost their first two pool games this season, that record is unlikely to improve in the near future. However, after a poor start to their domestic season, O'Shea believes it was Quins' battling performance in their 23-16 loss to Clermont Auvergne in October that energised his players and turned their Aviva Premiership form around. After four consecutive wins, they now sit fourth in the table.
"We all want to be playing in Europe," said O'Shea. "We want to be there. We had a poor start to the season, but the competitive juices started flowing after Clermont. These are the matches you want to play in because of the he atmosphere, the hostility, the quality of players you are up against. Our guys would really miss it if they were not involved in those big games, and hopefully there is still a chance they will be.
"The players enjoy it because it is a break from the norm. It is just fun for everyone. In your own league, you can always tell what is going to happen from one week to the next, but it is less predictable when you go into Europe. Everybody wants it. So many of the hurdles have already been crossed in terms of qualification and distribution of finance. Everyone seems to be in agreement, so let's just get across the line. Maybe someone will have to swallow their pride a bit, but it is better for the game and that's what we all want."
Just as O'Shea wants his players to be widened by their exposure to the best of the Celtic, French and Italian sides, the learning process works both ways. There is a hard-nosed pragmatism about English rugby that is not always part of the mix in the RaboDirect PRO12 league, and it is valuable experience for Edinburgh and Glasgow players to come up against it.
The beauty of the Heineken Cup is in its rich and diverse tapestry. Rather than gloat at the pickle the English clubs have got themselves into, the sport should do everything to bring them back on board.