The Central Land Council wants Henbury Station returned to traditional owners.
The station, 230 kilometres south of Alice Springs, was bought by R. M. Williams Agricultural Holdings with $9 million of federal funding in 2011.
It was destocked with the intention of re-generating the property for carbon credits, whilst forming part of the National Reserve System.
this week after R. M. Williams Agricultural Holdings went into receivership last month.
Central Land Council director David Ross says it's seeking assistance from the Indigenous Land Corporation to buy the property.
"We'd really like to see the Henbury title returned to the traditional owners, the Pertame people, that have had this association with this land since forever," he said.
"We think it's time they actually got title to it, not just native title.
"Upfront traditional owners weren't given an opportunity.
"Considering how much the Commonwealth spent it would be lovely if to have it gifted, but I think that might be a long shot so we're in the process of talking to the Indigenous Land Corporation and others about how we might be able to go about acquiring some funds to help purchase it.
"I think they [traditional owners] would feel absolutely robbed if they were left out of this process after what the Government has done."
Mr Ross says the Indigenous Land Corporation is supportive of the purchase, but has not yet committed any funding towards it.
He says traditional owners are interested in both cattle production and carbon farming on the property.
"A lot of the family members would be more than happy to be involved in the pastoral industry.
"But people are open to whatever opportunities there are.
"If there's work there and jobs for family members, people would be more than happy to look at both."
The Northern Territory Government say they .
Mr Ross says this is short-sighted.
"Why would you cut off your nose to spite your face?
"At the end of the day if there are opportunities, then they should be open to carbon farming, if the ability is there to do so."
The Central Land Council is developing a native title claim for Henbury Station on behalf of traditional owners which is expected to be submitted for assessment in the next six months.