The government is reportedly working on a pact with Afghanistan to return asylum seekers, whose applications for asylum have been frozen.
The agreement will involve assurances from Kabul guaranteeing the safety of unsuccessful asylum seekers, The Australian reports.
But it is unlikely to be announced this week under Labor's revised border security policy.
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Labor frontbencher Mark Butler refused to deny the report, telling Sky News only that "the situation in Afghanistan is fluid".
But the Greens disagree, noting that 10 ethnic Hazaras were beheaded in Afghanistan the day Julia Gillard became prime minister less than two weeks ago.
"A deal struck between Julia Gillard and the Afghan government is not going to secure their safety," Greens immigration spokeswoman Sarah Hanson-Young told ABC Television.
"It's just Labor Party spin ... to continue down that low road of politics, chasing (Opposition Leader) Tony Abbott in a tussle to beat up on refugees.
"Julia Gillard should know better."
Cabinet will meet in Canberra later on Monday to nut out its revised policy for release ahead of Thursday, when the three-month moratorium on processing Sri Lankan asylum claims expires.
Parliamentary secretary for multicultural affairs Laurie Ferguson told ABC Radio a "sensible middle position" will be "very difficult" to reach.
At the same time outgoing Labor MP Julia Irwin has asked her colleagues not to get nasty.
"I hope they (Labor MPs) don't start using the abusive terms used by some commentators," she told ABC Radio.
The opposition says the government's new position will be insincere and lack authenticity.
"It's all about a false midnight conversion on the eve of an election and I think the Australian people see through that sort of lack of authenticity," opposition immigration spokesman Scott Morrison told ABC Radio.
A raft of measures, including temporary protection visas, offshore processing and turning back boats, was needed, he added.
Liberal senator Mitch Fifield also criticised the government's approach.
"Under this Labor government there has been demonising of Australians who have expressed genuine concern on asylum seekers," he told Sky News.
