Former Reds' coach McKenzie, who led the franchise to its first and only title in 2011, has seen off the challenge of Brumbies' mentor Jake White, a South African World Cup winner with the Springboks.
Lions' coach Warren Gatland, like Deans a New Zealander, said he empathised with the former Crusaders' coach.
"I've got a huge amount of respect for what Robbie's achieved in rugby," he told reporters on the weekend.
"I know it's been really tough for him being here. There's a lot of people split about whether he should carry on the job.
"It's tough to have a Kiwi involved coaching an Australian side. I admire him for what he's achieved in rugby.
"We often sit down after games and have a chat and a beer together. We had a brief chat (on Sunday) night. He said he might get to see us in November, but that depends on what happens in the next few weeks."
Australian Rugby Union chief executive Bill Pulver said on the weekend that he wouldn't rush into a decision about Deans, but following interviews with McKenzie and White, he appears to have done exactly that.
Pulver said "there has been a lot of emotion and comment expressed from various areas ... we will not be entering into any speculation or debate on the coaching issue at this stage".
Deans presided over 74 tests since crossing the ditch in 2008, leading the Wallabies to 43 wins, 29 losses and two draws, for a winning percentage of 58 per cent.
His record against South Africa was very good - nine wins in 14 tests - but he failed to get consistent results against the All Blacks. In 18 attempts, he managed just three wins. Australia also twice lost to Scotland under his reign.
- nzherald.co.nz