Queensland Reds coach Ewen McKenzie has confirmed he would be interested in becoming the new Ireland boss, following Declan Kidney's departure.
Kidney left his post on Tuesday when the Irish Rugby Football Union decided not to offer him a new deal.
McKenzie has been linked with the Ireland role since announcing he would step down as Queensland coach at the end of the current Super Rugby season.
But Harlequins director of rugby Conor O'Shea said he was not a contender.
And Saracens chief executive Edward Griffiths has dismissed any prospect that Mark McCall, a former Ulster coach, could be in the frame.
Kidney led Ireland to the Grand Slam in 2009 but departed after a poor 2013 Six Nations campaign.
Ireland lost to England, Scotland and Italy to finish fifth and have also dropped to their lowest ever world ranking of ninth.
Former Australia prop McKenzie has a stated desire to coach the Wallabies - but he also recognises his chance to work in Test rugby may have to come elsewhere.
McKenzie told Sydney's Daily Telegraph he had not been in contact with the Irish Rugby Football Union - but he also left the organisation in no doubt he would be interested in a conversation.
"I have said I am looking for coaching challenges at the next level and I am looking for whatever the possibilities are," said McKenzie.
"It is the type of job I am 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.
"I have made it clear the challenge of coaching at that level is what interests me but there are not many opportunities at Test level and you can't control the timing."
Former Ireland full-back O'Shea insisted that even the lure of coaching his country was not enough to turn his back on a project at Harlequins he believes still has a long way to run.
"I am going nowhere. My contract is here [until the summer of 2014], I love it here and hopefully I will be here for a long time to come," O'Shea said.
Joe Schmidt is a strong contender for the post having guided Leinster to back-to-back Heineken Cup triumphs with one of the most scintillating attacking teams in Europe.
The New Zealander has one more year on his current Leinster deal, having signed an extension last September.
Les Kiss, Ireland's defence coach who worked with McKenzie at the NSW Waratahs, will step up to be interim Ireland head coach for the summer Tests against the United States in Houston on 8 June and Canada in Toronto a week later.