Fairfax Media, citing "confidential bank documents", has reported that Paraka regularly transferred large sums of cash to contacts on the Gold Coast and in New South Wales - including one payment in October of about $80,000 to his wives and girlfriends based in Australia - where one lived at Sydney's Star City casino complex.
The report further claimed that one of Paraka's PNG banks had a business relationship with National Australia Bank.
When asked for comments on the report, a NAB spokesman re-issued the statement it previously made to Fairfax.
"In late 2012, NAB heightened our due diligence relating to some funds from PNG, as a result of information that became available to us through official channels in PNG," the spokesman told PNGIndustryNews.net.
"National Australia Bank takes all allegations of money laundering seriously. Payments that NAB deems as suspicious will be blocked and reported as required by law. We work closely with regulators and police in both Australia and PNG in enforcing anti-money laundering laws."
The NAB official said he could not comment on specific payments made on behalf of individual customers. It was unclear if any action was taken against Paraka.
Fairfax also questioned what Australian banks, the Australian Federal Police and funds transfer watchdog AUSTRAC were doing to investigate or block "dirty money" transfers.
An Australian government spokesman told PNGIndustryNews.net that AUSTRAC could not comment on the matters raised in this report.
"As we have in the past, we can provide broad information about the agency's intelligence and regulatory role, but we are unable to comment on individual intelligence or operational matters," the spokesman said.
Opposition Leader Belden Namah questioned in a May parliamentary session why a K71.8 million ($A34.6 million) payment was made to Paul Paraka Lawyers. Prime Minister Peter O'Neill has since threatened to sack finance department staff, as well as seeking AFP and Interpol assistance.
AFP senior liaison officer Superintendent Steve Mullins claimed that month that PNG politicians and bureaucrats were siphoning half a billion kina a year into Australian banks.
PNG's Ombudsman Commission, often criticised for not taking suitable action against politicians, has a new official chief ombudsman following the death of his predecessor in 2011.
O'Neill announced the appointment of Rigo Lua to the role this week. He is a nephew of Public Services Minister and former Somare government mining minister Sir Puka Temu and former Chamber of Mines and Petroleum chairman Dr Ila Temu, reports the Post-Courier.
The newspaper separately reported that PNG's specialist police unit Task Force Sweep had arrested a public official from the Department of National Planning and Monitoring. The bureaucrat allegedly defrauded the state by forging documents awarding a K3 million contract to United Builders & Contractors Limited.
Blog PNGExposed has also reported that Task Force Sweep has shrunk from a core investigative team of 15 staff to just four, including its chairman Sam Koim, the police prosecutor and two other policemen.