Fairfax Media reported that those returning to Lebanon from detention centres on Papua New Guinea's Manus Island and the tiny Pacific state of Nauru were offered the highest amount of AUD 10,000.
Iranians and Sudanese were given AUD 7,000 if they dropped bids for refugee status, Afghans AUD 4,000 and those from Pakistan, Nepal and Myanmar AUD 3,300, the report in The Sydney Morning Herald said.
The Herald said under the previous Labour administration - in office until last September - the payments were much lower, ranging from AUD 1,500 to AUD 2,000.
"The process of voluntary return is conducted in direct partnership with the International Organisation for Migration. It has been standard policy and practice for more than 10 years."
Labour's immigration spokesman Richard Marles said the government should be ensuring that asylum-seekers' claims were being properly processed, not issuing "blank cheques".
"When Scott Morrison was in opposition, he opposed Labour's own reintegration packages and now he is offering sums which are triple the amount," Marles told the ABC.
Instead they are held in detention camps on Manus and Nauru and are expected to be resettled in those countries if their claims are valid.
Since the policy was introduced, more asylum-seekers have chosen to voluntarily return to their country of origin while the number of people attempting to reach Australia by boat has dried up, with no boats arriving for six months.
Morrison's spokesman said 283 people had voluntarily returned home from offshore processing centres since shortly after the conservative government of Prime Minister Tony Abbott won power in September.