Howard, a strong critic of the regime of Zimbabwe President Robert Mugabe, said it was not entirely clear whether his government could legally direct the national team not to tour the strife-torn southern African nation.
"I am jammed between my distaste for the government getting involved in something like this and my even greater distaste for giving a propaganda victory to Robert Mugabe," Howard told Australian radio.
"Obviously, if there is a way legitimately that the tour can be cancelled and there not be an exposure by Cricket Australia to any fine, then we'll go down that path."
Foreign Minister Alexander Downer met Thursday with officials from Cricket Australia, which face a US$ two million fine imposed by the game's governing body if they abandon the tour.
Howard, a keen cricket fan, called on the international cricket community to stop giving comfort to Mugabe's regime by allowing teams to tour his country.
"I think the International Cricket Council has responsibilities, yes," Howard said. "But they're like any other body - they're answerable to their constituent members.
"Now, I think there is some evidence emerging that even in those countries that would be very reluctant to see the ICC do anything, that something ought to happen.
"How long can the international cricket community - not just Australia - go on doing things that give aid and comfort to somebody who has thus far been totally impervious to any entreaties?"
Howard said he had raised the issue with Australian captain Ricky Ponting at a welcome home breakfast for the victorious World Cup team last week.
The issue on whether to tour Zimbabwe has become a hot topic in Australia, with church groups urging a boycott.
The nation's 42 Catholic bishops saying such a move would be a significant symbolic gesture against an oppressive regime.
The Catholic aid agency 'Caritas Australia' said that if the government paid the fine, it should insist that the ICC order the money be held in trust for cricket purposes to ensure it did not go to Mugabe's government.
Fast bowling great Dennis Lillee joined the growing chorus of voices calling on Australia not to tour Zimbabwe.
"You cant endorse a regime like that," Lillee told the West Australian newspaper.
"That is what (the tour) may seem to be doing. It is not a place I would recommend Australia should tour because of the political problems there."
Lillee, the WA Cricket Association president, said he was speaking as a private citizen, and not as a cricket administrator.
"There are obvious grounds not to tour though you have to feel sorry for the Zimbabwean players."
Former Zimbabwe coach and Australian batsman Geoff Marsh questioned the value of an Australian boycott.
"The feeling I get -- and it's the opinion of some of my Zimbabwean mates as well -- is what difference will stopping a cricket tour make?" Marsh told the Sydney Morning Herald.
"Whether it's the right or wrong thing to do is another matter, but, in real terms, I just wonder what it will achieve.
"I generally don't like to see sport and politics mix. I think strong action definitely needs to be taken.
"But I think it has to happen in areas broader than just sport. It is a beautiful country that has become a living hell for a lot of people."