The family of six is thought to be camping temporarily on an uninhabited island in Australian waters after arriving there at the weekend, two Australian newspapers reported on Wednesday.
John Howard, the Australian prime minister, said the reports had yet to be confirmed.
The reported arrival comes amid continued anger from the Indonesian government over Australia's decision to grant visas to another group of Papuan asylum seekers who arrived in the country last month.
Howard refused to say whether the new arrivals were likely to further exacerbate tensions with Jakarta or how the new asylum applications would be processed.
"I am not going to engage in running speculation," Howard told reporters.
Howard also reiterated that he believed the province, which is also known as West Papua, should remain part of Indonesia despite the long history of its separatist movement.
"My message to the people of West Papua is simply this: I regard them as citizens of the Republic of Indonesia," Howard said.
"I have a very strong view that the best resolution of these issues is within the sovereignty of the Republic of Indonesia over West Papua."
Indonesia has protested that Australia gave asylum to 42 Papuans despite the assurances by Indonesia's president that they did not face prosecution at home.
"Clearly this has created a strain in the relationship, but I don't regard it in any way as a fatal strain."
John Howard, Australian PM
Jakarta recalled its ambassador to Australia, and the normally feuding political elite united in outrage at the decision and repeated its insistence that Papua belongs to Indonesia and claims of human rights abuses there are a fiction.
The Papuans claimed that Indonesian troops were committing genocide in their homeland which became part of Indonesia in a now discredited UN ballot in 1963.
"Clearly this has created a strain in the relationship; but I don't regard it in any way as a fatal strain," Howard said.
"I think the relationship is strong enough and deep enough and warm enough to survive this; but it is an issue about which the Indonesians feel a great deal of sensitivity," he added.
Respect for Indonesian sovereignty has been a sensitive issue since Australia led UN peacekeeping troops into East Timor in 1999 after the then Indonesian province voted for independence.
The government of John Howard decided on 23 March to grant temporary protection visas to 42 asylum seekers, who arrived in Australia in a dugout canoe claiming that Indonesian troops were carrying out a policy of genocide in their homeland.
Indonesia's furious reaction to the decision illustrates its fear that the province may one day break away from the sprawling nation, as East Timor did in 1999.
Keeping hold of the resource-rich province is seen as vital because its independence could inspire other regions in the ethnically diverse island country to shake off Jakarta rule, leading to the eventual disintegration of the country.