Multiple players have raised concerns over the women's schedule in recent weeks, which includes four straight years of no home internationals or WBBL in school holidays.
Ellyse Perry and Beth Mooney have also highlighted fears it will stunt the growth of junior cricket, with the women's team out of sight and out of mind.
Australia play Bangladesh and New Zealand in three ODIs and T20s respectively over the next fortnight, before a home ODI series against New Zealand in March.
Chief among the concerns of players is a lack of consistency in their schedule to build up crowds, along with games on school nights that families largely won't attend.
The issue was raised at a function on Monday night in Brisbane to recognise the Australian team's T20 World Cup win.
"We're looking at that actively," CA chief Greenberg said.
"(Head of cricket) James Allsopp led the conversation with the Australian women's team about this exact issue, so we're talking, we've got dialogue with them.
"We would love to see more cricket played in this window. We have to understand the global components ... but we've got to get more cricket into our summer."
Multiple players have also privately expressed concerns to AAP over India being handed the January window for the lucrative WPL, effectively blocking out part of the calendar.
In the players' view, the fact Australia provides several of the biggest names to the tournament could have been used as leverage by CA.
Greenberg was hesitant to comment on negotiations carried out by previous administrators, but insisted there were other ways to give the game appropriate air.
One option would be to push the WBBL final back into mid-December, while another is regular internationals in the lead-up to Christmas.
"We're looking at that actively, but the challenge is always how do you get the best opposition to come and play and commit to that window," Greenberg said.
"We've seen when a men's Test match is played during the day, the BBL game at night is significant.
"So imagine a world where there's a men's Test match that runs into an Australian women's team's international or a WBBL game. That would be really good.
Greenberg's comments come after Mooney was particularly critical of the current schedule.
"We're in a bad timeslot and it's a bad time of year for parents," Mooney told AAP.
"They're not dragging their kid out to watch a 7pm T20 on a Tuesday night or whatever it is.
"We're not getting crowds, it's not marketed well. There is no big-ticket item where people go 'the Australian women's team play here at this time every year'.
"We want to be relatable athletes. And if we're not front and centre of the summer, it makes it pretty difficult when it's meant to be a summer sport."
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