During a debate over last year's financial statements on Monday night, independent councillor Dom Figliomeni asked other councillors to consider allowing an independent contractor to undertake a "financial health check" of the council.

Cr Figliomeni said he wanted to "give confidence to the Wollongong community that council is in a financially stable position", and raised concerns about the adoption of two new policies - the long-awaited cycling strategy and climate change mitigation plan - that he said would cost the city hundreds of millions of dollars over the next decade.

"There are two items on tonight's [agenda] which together account for a significant expenditure going forward," he said.

"Not only do we have $32 million expenditure over two years in climate mitigation, but also ... we have a cycling strategy which has an estimate of $200 million over ten years, [an] average of $20 million per annum."

He said he did not know where the council would get the money to fund the items in these two documents.

Liberal John Dorahy was the only councillor sympathetic to Cr Figliomeni's request - although he eventually voted it down - noting the council would have been in a "negative financial position" last year had it not received government grants.

But Greens councillor Mithra Cox said suggesting the council was in bad financial health was "offensive and problematic".

"I find it kind of ironic that you would stand up here and criticise the financial health of the organisation and simultaneously propose an uncosted consultant to come and write a report for us that has not been discussed in any of our budget considerations," she said.

She said the annual statements showed the council has met "almost all" of the NSW government's benchmarks for financial health for councils, and said those where the council hadn't met the benchmarks had been because of special provisions it had made for ratepayers during COVID-19.

As for the adoption of the two new plans which commit the council to spending over the next decades, Cr Cox said it was "frankly ridiculous" not to plan to build new cycleways or meet climate change challenges based on a lack of knowledge about the council's future finances.

"There are many uncosted items in many of our plans, it doesn't mean that we are obligated to fund them - but the fact they are in a plan means we can apply for funding when it is available and that is how we are funding the majority of our cycling plan," she said.

"Unless we have a plan, we don't have the opportunity to have that money from the government."

Labor councillor Ann Martin noted that the Blue Mile plan was unfunded when it was first adopted by the council, but had been progressively built using government grants and council funds over a decade.

Also disagreeing with Cr Figliomeni, Janice Kershaw said the council had been presented with an independent audit of its financial statements during the October 26 meeting.

She said Cr Figliomeni had the opportunity to raise any concerns about the council's finances then, but did not do so.

Her colleague, Jenelle Rimmer noted that the audit office "did not respond saying we have somehow cooked the books".

"We have been prudent in making decisions that are considered, because we are well aware that we are using ratepayers funds," she said.

"To somehow say that our accounts might be unhealthy is offensive and completely untrue.

"It's a terrible message to send to the community. It's an absolute shame that we have a councillor that's willing to stand here and say that to the community. I'm gobsmacked."