The auditor-general is considering investigating a federal government decision to give a contract to a US prison company accused of fraud and pandemic profiteering.
Prison provider MTC Australia will be paid $69 million for four months' work to run garrison and welfare services for asylum seekers in Nauru.
Their parent company is being investigated by the Texas Department of Criminal Justice, and has previously been accused of security failures that led to murders and rapes.
Greens senator Nick McKim wrote to the auditor-general asking to investigate Home Affairs' decision and what due diligence the department had done checking MTC's parent company.
He also asked them to investigate if MTC was an appropriate company to engage given the previous issues, and if Commonwealth procurement guidelines were followed.
"Some or all of these allegations were known to, or should have been known to, the Department of Home Affairs at the time it decided to enter into or extend arrangements with MTC Australia," Senator McKim wrote.
A Home Affairs spokesperson said all procurement rules were followed when awarding MTC the deal.
"Transitory persons under regional processing arrangements in Nauru are managed by the government of Nauru, with support from Australia through the provision of contracted service providers," they said in a statement to AAP.
"The department is finalising procurement processes for regional processing capability services to support the government of Nauru."
There are fewer than 100 asylum seekers on Nauru, although MTC's contract does not involve any detention.
Senator McKim said offshore detention was a "decade-long humanitarian calamity which has wasted billions of dollars of public money".
"The Department of Home Affairs has an abject record on transparency, probity and good governance, and there is a very strong case for the auditor-general to investigate how this company came to be engaged given the seriousness of the allegations its parent company is facing," he told AAP.
"We should be offering immediate resettlement in Australia to everyone still stranded on Nauru and in Papua New Guinea."
MTC's president Dan Marquardt welcomed the contract in a post on his company's website.
"This is an opportunity to serve those that are moving through the immigration process with dignity, care, and respect."