Last night the Sydney Morning Herald reported Colt was held at Sydney's Villawood detention centre and had appealed her deportation, meaning it could be delayed for months.
Colt was part of a 40-strong group that lived in squalid conditions near Canberra.
In 2012, authorities took away 12 children from the group and later testing revealed that only one had parents that were not related.
The children, who were under-fed, hardly went to school and lacked basic skills such as how to shower and clean their teeth, later told of suffering sexual abuse.
A judge ordered Colt's five children aged under 16 were to be put in foster care.
He noted the case appeared to be one of intergenerational incest and Colt may well have been a victim of incest herself. According to previous reports, Colt's mother's parents were brother and sister.
Her mother and her husband moved from New Zealand to Australia in the 1970s.
In 2013, Colt was sentenced to a year in jail after she tried to recruit one of her sons, aged 15, to help her abduct his brother from state care. No one in the family has faced any incest-related charges.
Labour has criticised the Government as too slow to lobby Australia on the issue and to act on how to deal with the influx of deportees.
Leader Andrew Little said the Colt deportation - if confirmed - demonstrated the problems with current deportations.
"Australia is where she has lived the bulk of her life. You just wonder if it is serving anyone's interests for her to be sent back here."
Last month Justice Minister Amy Adams announced the signing of an information-sharing agreement with Australia that would provide more details on criminals being sent to New Zealand.
At the time, Ms Adams said the next step was a law change to ensure prisoners arriving here would be subject to the same controls and supervision as they would had they served their sentence in New Zealand.
After meeting Mr Key on the weekend, Mr Turnbull declined to lower the threshold at which Kiwis were deported.
He promised he would put more resources into the appeal process so it could be carried out more quickly, and to clear a backlog that had resulted from the law change in December.
Yesterday, Mr Key said the more than 200 Kiwis held in seven Australian detention centres - including on isolated Christmas Island - could return to New Zealand as soon as they wanted and have their appeals heard from here.
He accepted many would be sceptical that they would be "out of sight and out of mind" if that happened, but said he had been assured their cases would be treated exactly the same as if they were on Australian soil.