Kidney left his post on Tuesday after the Irish Rugby Football Union decided not to offer him a new deal when his current contract expires on June 30.
Harlequins director of rugby Conor O'Shea today ruled himself out of contention and Saracens chief executive Edward Griffiths said Mark McCall was committed to his club.
McKenzie has been linked with the Ireland role since announcing he would step down as Queensland Reds head coach at the end of the current Super Rugby season to pursue a job at international level.
The former Australia prop 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," McKenzie said.
"It's 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 aren't many opportunities at Test level and you can't control the timing."
O'Shea was immediately tipped for the job, having guided Harlequins from the Bloodgate saga to Aviva Premiership champions and into this weekend's Heineken Cup quarter-finals against Munster.
But the former Ireland full-back 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'm 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.
"We just can't wait to get into the Heineken Cup quarter-final this weekend and help this club get to the first semi-final in its history.
"We are very excited about the group of players we have and how far we still have left to improve as a team.
"There are so many good young players at this club pushing the more senior statesmen. You look at the team that won the LV= Cup. You want to be around and see that grow.
"It is bloody exciting. Of course you are flattered (to be linked) but my job is here."
O'Shea has also been linked with the newly created role of England's head of international player development - another he position he stressed is not for him.
"There are better qualified people than I to take those jobs," O'Shea said.
Joel 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 head coach for the summer Tests against the United States in Houston on June 8 and Canada in Toronto a week later.
Kidney led Ireland to the Grand Slam in 2009 but he departed after a poor 2013 RBS 6 Nations campaign.
Ireland lost to England, Scotland and Italy to finish fifth and drop to their lowest ever world ranking of ninth.