Admitting he has become a "little unpopular" since taking over from Nick Hockley in March, the former Australian Cricketers' Association boss believes "scarcity in Test cricket is our friend, not our foe".
"I don't think everyone in world cricket needs to aspire to play Test cricket, and that might be OK," Greenberg said on Wednesday with 100 days to go before the Ashes.
"A lot of traditionalists might not like that.
"I'm not suggesting I know the number that will play, but literally we're trying to send countries bankrupt if we force them to try to play Test cricket.
"We need to make sure we invest in the right spaces to play Test cricket where it means something, and has jeopardy, and that's why the Ashes will be as enormous and as profitable as it is because it means something."
But there could be more Test cricket played in Australia, with Greenberg open to playing red-ball matches in Queensland and the Northern Territory during winter.
Australia are currently hosting South Africa in Twenty20s and ODIs in Darwin, Cairns and Mackay.
Tests were last played in Darwin and Cairns more than 20 years ago, with Australia hosting Sri Lanka in 2003, then Bangladesh the following year.
"I was in Darwin on Sunday night (for the first T20)," Greenberg said.
"I went there primarily because it meant a lot to the people of the Northern Territory.
"They hadn't had international cricket there for the best part of 17 years.
"The one thing when you go there at this time of year is you take the one biggest variable away, which is the weather.
"Great facilities ... I can see that (Tests) happening."
Greenberg has also been exploring privatisation of the Big Bash League, noting other T20 competitions around the world are backed by money outside the governing cricket boards.
"That will upset some people, and it will set the hares racing and potentially of people debating the merits," he said.
"It would be completely naive of us sitting here in Australia to not explore it.
"I'm not suggesting that we're going to do it yet.
"I'm not suggesting there's been a decision made, and ultimately it won't just be my decision or Cricket Australia's decision.
"It will be the whole of leadership of Australian cricket and it has to be beneficial for everyone."
