Greenberg argued that staging the fixture in India would help reignite interest in the longest format, describing the Anglo-Australian contest as one of the sport's most historic and commercially valuable rivalries.
He said the concept deserved serious consideration despite the teams traditionally meeting only in the Ashes.
"It's not something that we are planning, but it's open for consideration. We'd have to be open to considering all options," Greenberg said.
"Our relationship with the ECB and the BCCI is very strong and clearly there are opportunities in India to put more content in certain areas."
The Ashes is played on a rotating home-and-away schedule, with each nation hosting the series roughly once every four years.
Before any potential match in India, Australia and England will meet in a standalone Test at the Melbourne Cricket Ground in March 2027 to commemorate the 150th anniversary of the first Test between the countries.
Any proposal to stage the contest in India would require approval from Cricket Australia, the England and Wales Cricket Board and the Board of Control for Cricket in India.
Cricket Australia is also taking the Big Bash League abroad for the first time, with Melbourne Renegades facing Perth Scorchers in Chennai in December as it seeks to broaden the tournament's reach and capitalise on India's vast cricket audience, where Test cricket has lost ground to T20s and the IPL.
Steve Smith is feeling excited for the challenge ahead of Australia's busy Test schedule, starting next month at home against Bangladesh, according to chairman of selectors George Bailey.
Jacob Bethell is a doubt to start for England in the first Test against Pakistan next month after withdrawing from the Hundred due to a knee injury.
Pat Cummins, Josh Hazlewood and Nathan Lyon have all returned to a strong Australia squad for the two-match Test series at home against Bangladesh next month.
Brendon McCullum says he is looking forward to working with new England Test coach as they look to achieve success in all three formats of the game.
