Virgin Australia wants to allow small cats and dogs in the cabin under strict conditions.
Animals would not be allowed to roam around the plane or sit on passengers' laps, instead they would have to stay in an airline-approved pet carrier under the seat in front of their owner.
Only passengers in certain rows would be allowed to bring their furry friend onboard and they would have to pay for the service.
The airline has not revealed details of the plan including how much it would cost but hopes the change will happen within 12 months, once it is ticked off by regulators.
Virgin Australia chief executive Jayne Hrdlicka said the arrangement worked well overseas, as pets are commonly allowed on flights in North America.
"Overwhelmingly, our guests tell us they want to travel with their pets and we are now on a journey to make that a reality," she said.
Melbourne Airport chief executive Lorie Argus expects the plan to be popular with passengers.
He said pets would have to stay inside pet carriers at all times in the airport.
There would be no changes to existing arrangements for approved service animals and passengers travelling with animals could still pay for them to be transported as cargo.
The Civil Aviation Safety Authority has been contacted for comment.
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