Any tour would assume a high profile as Australia's national team won the just-concluded World Cup in the Caribbean.
The Voice of America Friday said the government does not want to be seen in any way as supporting the Mugabe regime, which has been accused of massive human rights violations and destroying the African country's economy.
Foreign Minister Alexander Downer has even offered to pay the $2 million fine that might be imposed by the cricket's world governing body if the tour is canceled.
"Back here in Australia, there's no doubt that in Zimbabwe, President Mugabe and his regime would make propaganda capital out of such a visit," Downer told the VOA.
Australian cricket executives were quoted a saying the issue is difficult and complex. They said while they are aware of the government's concerns, they also have to meet international obligations.