But the government says it "remains committed to delivering a long overdue new hospital in Dunedin, as soon as possible".
The warning comes as the government moves to replace the project with either a scaled-down version, or a retrofit of the present Dunedin Hospital.
The last of the piles have already been drilled for the inpatient building, but the construction site is sitting largely empty while the government considers the options.
When the project was first announced in 2017, the cost estimate was $1.2 billion-$1.4b - the government has recently said it would cap the cost of the project at about $1.9b.
Mr Olsen projected the inflationary rate for this quarter for the new Dunedin hospital build would be 0.6%.
"Given that everything is sort of just waiting around and everyone is twiddling their thumbs, it doesn’t seem like the best use of money."
The "ballpark" figure could be upwards of $10m of additional cost per quarter if nothing happened on site, Mr Olsen said.
"I think even the powers that be won’t want to see things take too long, both from the idea of getting some certainty for those across the lower South Island, but just as importantly from a government finances point of view to understand what actually are the implications here.
"It does still sort of beggar belief, the lack of details that continue to plague the Dunedin hospital project.
"The fact that some of these costs and some of these plans and so on haven’t already been done after all of the work that has gone through."
"Any project that you change paths with, or change design or put delays into, just racks up the costs. There seems to be a demand to go back to the drawing board again."
Prof Gauld said the project was now a "mega-project fiasco".
"We’ve had political mismanagement. There may be lots of kind of competent management in there, but it’s the ability to collectively manage and drive the project through that is important. So that’s where it’s been a fiasco as well."
Prof Gauld said the government needed "to be much clearer about what its intent is".
"I know we’ve been getting these sort of messages that Dunedin will get its hospital, it’ll be $1.88b, but I think we need a lot more clarity than that, actually.
"We also need some assurances that it’s going to be really well managed, and we need to understand what the mechanism for that is."
The Otago Daily Times asked Health Minister Dr Shane Reti about whether the government had any concerns about the inflationary costs of the build, or whether it could deliver the hospital with the specifications promised in its 2023 election campaign within the budget.
Prior to the 2023 election, the National Party promised when the hospital opened, it would have 421 beds ready to go, and there would be 13 functioning main operating theatres - two more than the business case indicated - and the vital PET scanner would be installed and operating from day 1.
Dr Reti said the "government remains committed to delivering a long overdue new hospital in Dunedin, as soon as possible", but did not elaborate further.
