Since 2010, the primary school has been run in partnership between the Department of Education and Noel Pearson's Good to Great Schools Australia network under a Memorandum of Understanding.
The Department of Education has provided around $9 million to the school over six years, but says the current funding arrangement doesn't ensure "a return on investment".
"We’ve been trying to negotiate with Good to Great Schools for about 14 months," says Education Queensland Director-General Jim Watterston.
"We’re very keen to develop an agreement, but we want an agreement that has performance targets in it, and has milestones that need to be met."
Dr Watterston said despite significant investment, students weren't engaged in school, with the average daily attendance rate dropping to 50.8 per cent during the first term of 2016.
His comments come after the State Government moved to take greater control of the school in July, in response to a series of recommendations from a month-long review, undertaken after teachers were twice evacuated over safety concerns.
Education Queensland rejects claims it's "dismantled" school's teaching method
Speaking at forums hosted by the conservative Centre for Independent Studies in Brisbane and Sydney this week, Noel Pearson claimed the Queensland Government had "completely dismantled" Aurukun school's teaching pedagogy in recent months, undoing six years of progress.
Backed by Aurukun elder and teaching aide Phyllis Yunkaporta, Mr Pearson said the school's Direct Instruction teaching method, a closely tailored literacy and numeracy program adapted from the US, had been "abandoned", causing students to become disengaged.
Dr Watterston disputed those claims on Friday.
'We think the school is in great shape compared to what it was.'
He says Direct Instruction is still in place, and student outcomes have actually improved in recent months.
"Attendance at the school is better, the focus and certainly the behaviour and the management of the school site is incredibly better... and there’s community support so we think the school is in great shape compared to what it was." he told NITV.
"There’s a lot of growth left in the Aurukun school that needs to be harnessed and the potential of those kids realised.
"If you look at Indigenous outcomes in every state in Australia... it’s clearly accepted that we get the best Indigenous results on a state basis across Queensland.
"So the state school system, the Education Department in Queensland has got a fantastic track record. We know what we’re doing, we should be running state schools."
Dr Watterston said he didn't want to speculate about what would happen to the school if a new funding arrangement couldn't be reached, while Mr Pearson said the school's future remained a "great uncertainty".