Australia will consider pushing for Zimbabwe to be stripped of Test status at next month's International Cricket Council (ICC) meeting.
"It's over a month away right now and that gives the Zimbabwe Cricket Union (ZCU) a chance to resolve some of their differences with their players," Cricket Australia (CA) chief executive James Sutherland told a news conference on Saturday.
"I think that (the Test status of Zimbabwe) is a question that has probably come on to the table and is higher on the agenda now than it has ever been before."
Asked whether CA would lead a push to strip Zimbabwe of Test status, Sutherland said: "We'll obviously make a judgement a lot closer to the time.
"But there is no doubt that Cricket Australia and a number of other full member countries are concerned about how things have developed in recent weeks."
Zimbabwe's two-Test home series against Australia, the world's top-ranked team, was called off on Friday, 24 hours before it was due to start.
In an unprecedented move, the ZCU and CA agreed at a meeting in Harare to postpone the matches. Because of Australia's tight schedule, the games are highly unlikely to be played for at least four years.
FESTERING DISPUTE
Zimbabwe would have had to field a severely weakened team due to a festering dispute which has left the selectors without 15 experienced white players, including ex-captain Heath Streak.
However, three one-day internationals, originally set for June, are being brought forward to May 25, 27 and 29. All will be played in Harare.
The joint decision to call off the Tests came two hours before an ICC teleconference which looked likely to strip the series of its Test status. The teleconference was swiftly abandoned.
"One can't predict but one would assume that a Zimbabwe Second XI or Third XI playing against the best team in the world would not have been a pretty contest," Sutherland said.
"It's well known that the ICC have commenced a review of the structure of international cricket."
Sutherland said CA supported the ICC's review.
"The circumstances around this (deferred tour) are no good for the game of cricket. The game is not worthy of this kind of speculation and uncertainty," Sutherland said.
"There are certainly concerns about the standard of their team at the moment and that's something the ICC will address at their June meeting."
