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 30 June. Les Kiss, Ireland's defence coach, will be interim head coach for the two summer Tests in North America.
McKenzie became the mot capped coach in Super Rugby history last weekend when he was in charge for his 131st game in the tournament has been linked with the Ireland role since announcing he would step down as Reds head coach at the end of the current Super Rugby season to pursue a job at international level.
The former Australian prop, who had a brief spell coaching at Stade Francais Paris, 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 said he had not been in contact with the Irish Rugby Football Union, but he also left the organisation in no doubt he would be keen to have a chat with them about their new vacancy.
"I have said I am looking for coaching challenges at the next level and I am looking for whatever the possibilities are. It's the type of job I am interested in looking at but there have been no discussions," said McKenzie.
"I have stated I would like the Wallabies job but it's all in the timing. You have to look around at 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."
Saracens director of rugby and former Ulster coach, Mark McCall and Harlequins director of rugby Conor O'Shea have both ruled themselves out of contention.