A team from PricewaterhouseCoopers has been working to confirm the final figure since the review was announced by Mr Orders and Dunedin Mayor Dave Cull in February.
Mr Orders yesterday told the Otago Daily Times the review team was "almost done" and expected to finish its work next week, then present findings to him.
Mr Orders would then compile a report on the review's findings to be presented to the next full council meeting on May 14, where it would be debated in public.
"That's the commitment we've given," he said.
However, council governance manager Sandy Graham said, depending on the findings, the report might not be circulated as part of the public agenda in the days before the meeting.
Instead, it could be given first to councillors as a non-public report for them to consider, and then made public by the day of the meeting.
That was yet to be determined, but in either case the same report would be made public, she said.
Mr Orders would not comment when asked about the review team's findings to date, saying to do so would be "premature".
"I've not seen the report so I'm not in a position to reflect on whether or not there are major concerns."
Last month, he said the extra time being taken to complete the review was not an indication anything "untoward" had been uncovered.
Yesterday, Mr Orders reiterated it was important to take the time to "get the report right".
"They [PWC] have gone through a large amount of information, some historic information, and they've interviewed a number of individuals involved with the stadium project.
"It's just been time [spent] going through things."
The review announced last month sought to clarify unanswered questions that could add "millions" of dollars to the final cost of the venue, Mr Cull said at the time.
The results had been expected to be presented to last month's full council meeting, but the PWC review team's work was extended by two weeks on March 21.
