Kidney's five-year reign came to an end on Tuesday, leaving the National Team Review Group with the tough task of finding a replacement.
Ireland's backs coach Les Kiss has been appointed interim coach for the summer tour in June and could perhaps make the move permanent.
But the outright bookies' favourite is Queensland Reds coach Ewen McKenzie.
He guided the Reds to the Super Rugby Crown in 2011, but recently announced he'll be stepping down at the end of the season to pursue international ambitions.
And McKenzie does have top-level experience, having served as assistant coach to Australia for three years.
"I have said I'm looking for coaching challenges at the next level and I'm looking for whatever the possibilities are," he told Sydney's Daily Telegraph.
"It's the type of job I'm interested in looking at, but there have been no discussions.
"I have stated I would like the Wallabies job, but it's all in the timing. You have to look around what's available when you're looking for a job."
A host of other names are also being bandied about, but one man to rule himself out of the running is ex-Ireland international Conor O'Shea.
He's Director of Rugby at Harlequins and says he'll be both honouring his contract and hoping to see it renewed after next season.
"Of course you are flattered (to be linked), but my job is here," O'Shea said.
Outside odds are being offered for the likes of Brian O'Driscoll and outspoken pundit George Hook.
Kidney's successor is not expected to be confirmed until after Ireland's summer tour to the US and Canada.