Sources in Papua New Guinea have told the ABC the two main companies being considered are Transfield and Serco.
However, both reported frontrunners have been embroiled in scandals in recent weeks, with allegations of sexual assault on Manus Island and brutal 'fight club' videos filmed within a New Zealand prison.
The ABC understands Australia wants to hand over total control of the Manus Island detention centre to PNG authorities in the five-year period but is willing to extend the contract for an extra four years if that does not happen.
It is not clear if the same plans apply on Nauru.
"The proposed term of the contract is for an initial term of five years," a spokeswoman from the Department of Immigration and Border Protection (DIBP) said.
"The department may, at its sole and absolute discretion, extend the term of the contract by up to two additional periods of up to two years each."
The contract is expected to be worth several billion dollars.
A PNG company called Anitua is also being discussed for Manus Island but it is unclear if it is also bidding for the Nauru centre.
A decision is due in August and the new contractor will take over the role on October 31.
The Greens said the length of the contract was evidence the Government was not confident its offshore deterrent would continue to work.
"If the boats have stopped, why is the Government signing long-term contracts worth billions of dollars?" Greens senator Sarah Hanson-Young said.
"Clearly the Government's intention is to keep refugees locked up for many more years to come.
"These companies are making big profits out of detention camps and have proven that they can't be trusted to treat refugees humanely, while also implementing the Government's harsh deterrence policy."
A spokesperson for Immigration Minister Peter Dutton said: "The Government will take appropriate measures to support the ongoing operation of the regional processing centres for as long as the facilities are needed to deal with people smuggling and illegal people movement in the region."
In February 2014, Transfield Services won $1.2 billion to run "garrison support and welfare services" at Manus Island and Nauru for 20 months.
Serco, which previously operated the offshore processing centre on Nauru, currently runs prisons in New Zealand.
Last week, Serco New Zealand was fined $328,000 after six videos were posted online showing a bare knuckle 'fight club' amongst inmates at the Mount Eden Correctional Facility.
The prison officers union said company bosses knew about the fight for up to 18 months but did not take action, according to New Zealand media.
On Manus Island, local residents and police are angry that three expatriate men were allowed to leave the island following an alleged attempted rape and sexual assault in mid-July.
The three men worked for Wilson Security, which is a sub-contractor of Transfield Services, and were reportedly drinking with a young Papua New Guinean woman and two local men on the night of the incident.
Australia's Department of Immigration and Border Protection said the incident breached the code of conduct signed by the workers but there were no allegations of criminality at the time.
The allegations of attempted rape and sexual assault were made two weeks later.
Police are still investigating and have threatened to arrest the managers of the detention centre if the three expatriate men are not returned to PNG for questioning.
This week, PNG prime minister Peter O'Neill called for an alcohol ban and drug testing for expatriate employees on Manus Island.