CA chairman David Peever has turned down the Australian Cricketers' Association's request for independent mediation and there are fears the stand-off could potentially lead to a players' boycott of the showpiece Ashes series later in the year.
Hunt said the government was hesitant about being too interventionist in contract disputes in professional sport.
But he said there was scope to act as a mediator if the dispute looked likely to threaten the home Ashes series.
"If it got to a last-minute situation, I suspect that we would offer to provide good officers brokering between the parties, but there's six months between now and the Ashes," Hunt told the Australian Broadcasting Corporation.
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"I do not see either the players or the administration returning to the late 1970s where we had a second-rate team.
"The players love playing for Australia, Cricket Australia knows this is not just fundamental to sport, it is part of our national identity. I'm very confident they will reach an agreement."
Hunt added that while Canberra would offer to mediate if there was a "fundamental threat", "all the advice I have is that with six months to travel, the Ashes will be proceeding with a full Australian team".
The ACA has described CA's rejection of the players call for mediation as lacking in common sense.
"The CA strategy is to refuse to deal with the ACA and go directly to individual players to try and break the model," a spokesman said on Saturday.
"This is despite the players repeated insistence for CA to respect their request and mediate with the ACA.
"To refuse mediation at a time when it's the only sensible way forward shows a clear lack of common sense."
But the ACA is equally resolved to keep revenue-sharing, saying the system was not broken and did not need fixing.