The Central Asian country has been listed as one of the nations being weighed up to receive refugees from Nauru and Manus Island, particularly Hazara Afghans, The Australian reports.
"We are having conversations with other countries to support our offshore processing arrangements and when we're in a position to make relevant announcements, the minister for immigration will do so," cabinet minister Mathias Cormann told Sky News on Saturday.
Refugee Action Coalition spokesman Ian Rintoul said the government is desperate if it is considering Kyrgyzstan.
"It's best known internationally as a nuclear waste dump," Mr Rintoul told AAP.
"The Afghan refugees there are routinely resettled to countries like Canada."
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The Greens said Australia's asylum seeker policy is now verging on the ridiculous.
"What next?" Greens leader Richard Di Natale asked reporters in Melbourne.
"Are we going to send people to Mars?
"This is ridiculous that we would look for any option other than the most logical, humane and economically responsible option, which is to ensure we process people here in Australia and, if they are found to be genuine refugees, that they are settled here."
Labor said the government should make public which countries it is talking to and trust the opposition in consultations for a solution.
"Let's not make it a domestic political point-scorer game - people's lives are involved, it's too important," Opposition Leader Bill Shorten told reporters in Sydney.
However, Mr Shorten labelled a plan that saw just four refugees sent to Cambodia at a cost of $40 million as a failed experiment.
