The spotlight is beginning to shine on what might be called "Endapendent" TDs who are being courted discreetly by both the Minister for Finance Michael Noonan and Taoiseach Mr Kenny.
Mr Noonan has suggested a number of centre-right Independents are quietly supportive of the Government’s policies and indicated they could perhaps be counted on to side with the Coalition parties in future.
“There are a number of left-wing Independents who are very high profile. But there are centre-right ones whose profile wouldn’t be that high who have the same voting strength,” he told a Bloomberg audience on Wednesday.
Mr Kenny hinted at his admiration for certain Independents when he was quizzed about coalition options after the next general election in a radio interview earlier this month.
“I’ve heard a number of constructive suggestions from persons who are Independent,” was his tantalising suggestion.
Mr Kenny tied Fine Gael’s political fortunes firmly to its Labour Coalition partners at his party’s ardfheis, but it has been clear for some time he sees the next Government as a three-legged stool.
That’s because both coalition parties are entertaining the possibility of heavy seat losses. Mr Noonan talked about Fine Gael losing 16 seats and Labour 18 in a “devastating” election, but many around Leinster House regard that as a conservative estimate.
The support of Independents will undoubtedly be required if Fine Gael and Labour are to get another shot at the title.
The easy part is figuring out which Independents Mr Noonan is probably not referring to.
Government-supporting Independents do not have to agree with everything an administration does.
A famous example is the Gregory Deal, under which Dubliner Tony Gregory struck a £80 million constituency deal with Charles Haughey. It seems unlikely Mr Gregory's successor Maureen O'Sullivan would follow in his footsteps.
Like-mindedness in terms of political outlook is usually required.
For that reason, among those unlikely to receive a call from the Fine Gael leadership are: Mick Wallace; Catherine Murphy; Thomas Pringle; Seamus Healy and John Halligan.
Governments want Independents who are not fair-weather friends. Prominent Independent Mattie McGrath is regarded as volatile in that regard.
Finian McGrath quickly withdrew his support from the last Government over Budget 2009 measures.
The understated Kerry South TD Tom Fleming assured me "no overtures" had been made in his direction.
But could Mr Noonan and Mr Kenny could be thinking about TDs such as Michael Lowry; Noel Grealish; Michael Fitzmaurice (always talking about co-operation); Michael Healy-Rae and Stephen Donnelly? Even Shane Ross (reported personality differences aside) cannot be ruled out.
Another potential source of support might be disaffected former Fine Gael TDs Denis Naughten and Terence Flanagan.
And Lucinda Creighton, on the brink of setting up a new party, has made no secret of her desire to influence Government policy.
However, a shrewd word of warning about the sometimes fickle nature of Independent support came from Fianna Fáil finance spokesman Michael McGrath. He tweeted last night: "Min Noonan should examine voting records of current Independent TDs if he believes they will prop up a minority FG/LAB after next election."
