Opposition Leader Tony Abbott has played down suggestions he would appoint former prime minister John Howard as the next governor-general.
The term of current Governor-General, Quentin Bryce, expires next March.
Mr Abbott has indicated he does not expect Mr Howard will be a candidate for the position.
"I have enormous respect for John Howard, but he served almost 12 years in a very difficult and demanding job and I think he's really enjoying his retirement," Mr Abbott said.
"I'm on the record as saying I think former military personnel and former judges by and large make the best vice regal appointments."
Ms Bryce, meanwhile, has arrived in Papua New Guinea on a five-day visit.
She flew into Port Moresby and was welcomed by the unique sounds of a bamboo band from Bougainville island.
Ms Bryce is scheduled to meet her PNG counterpart, Sir Michael Ogio, and prime minister Peter O'Neill.
During the visit Ms Bryce will travel to Rabaul on New Britain Island and to Alotau on Papua New Guinea's eastern tip.
On Thursday, weather permitting, Ms Bryce will take part in Anzac Day commemorations at the village of Kokoda.
She will also visit numerous local initiatives that focus on education, health and violence against women.