A multi-million-dollar contract awarded to an infrastructure company to help set up the detention centre on Nauru has faced renewed scrutiny, after it was revealed a key document does not exist.

The Gillard government provided open slather to Transfield Services in 2012 to decide the scale and scope of the arrangement when it won the initial $24.5 million deal.

A freedom of information search found a key document needed to set up the contract, known as a brief, does not exist, raising questions about whether the deal represented value for taxpayers' money.

Former immigration official and former New South Wales auditor-general Tony Harris said the absence of a brief meant Transfield was able to dictate the terms.

"It gives Transfield the scope to write the script," he told Lateline.

"If you haven't written the script, Transfield will write the script, Transfield will tell you what you need, Transfield will tell you how much it's going to cost you."

The Immigration Department has previously explained there was no competitive tender process because of the urgency in restarting offshore processing and that it was still finalising costs even after the first asylum seekers arrived on Nauru.

The department said it went for a direct approach with Transfield, however it also said it invited other organisations to join the process.

Public management expert Janine O'Flynn from the University of Melbourne said the department's evidence had been inconsistent about how the contract was awarded.

"There's some mention of going to an existing panel. There's some mention of going out to the market. There's some mention at different points about going directly to a provider," Ms O'Flynn said.

"So the sequence of events are not very clear."

Earlier this year the Abbott Government extended the Transfield contract to cover both Nauru and Manus Island to the tune of $1.2 billion.

"The [Commonwealth] auditor-general ought to be looking at this because poorly arranged contracts back in 2012 appear to have continued right through to 2014," Mr Harris said.

"It should go to a proper worldwide tender with proper briefs and a proper process."

The Transfield contract for Nauru and Manus Island is due to expire in October 2015 and a full public tender is expected for the next round.

Immigration Minister Scott Morrison emphasised the initial contract was awarded under the previous government.

"The Minister notes the explanation provided by the department secretary and does not propose to take any further action," he said.

Chris Bowen, the immigration minister at the time, said he was confident the department had acted appropriately.

Transfield Services declined to comment.