Stuff.co.nz reported Hansen made the comments at a Circa Theater fundraiser in the capital where he was being interviewed by former Kiwi television presenter Ian Fraser.
Fraser referenced a quote from Wallabies legend Mark Ella that "Mickey Mouse could coach the All Blacks to victory" because of the quality of the players at Hansen's disposal.
In a strongly pointed barb at his rival coach ahead of the World Cup, Hansen responded by saying: "They've got Mickey Mouse coaching Aussie."
The 2015 World Cup-winning coach went on to detail some of the ways the All Blacks have tried to get under Cheika's skin in their recent encounters.
"Michael Cheika, who by the way isn't a bad bloke, he just gets a bit emotional, and as you well know we thought we'd get him emotional and take his mind off the job," he said.
"The plan was not to call him by his name but just say he's the Australian coach. Then he went on a tirade about not respecting him.
"I guess what we're trying to do there is take his mind off the job and while I say he's not a bad bloke, he's got to control his emotions. I think he's got a good side, he does a good job of the coaching, but sometimes he just lets himself down there."
It's not just Cheika who has been the target of some mental warfare by Hansen, with the Kiwi admitting playing mind games with Warren Gatland during the 2017 British and Irish Lions tour.
"We probably had him where we needed him and then the bloody (New Zealand) Herald made a picture of him as a clown, which I didn't think was right, so I had to back off."
New Zealand Rugby has been contacted for comment.