The major energy project, which was announced under former coalition prime minister Malcolm Turnbull in 2017, is expected to play a key role in Australia's clean energy transition.
High construction costs and other challenges have already pushed back the 2021 completion date and blown out the $2 billion originally estimated cost of the project.
A report in the Nine newspapers suggests the cost of the project has blown out to more than $12 billion, based on sources familiar with the details of an internal review into the matter.
Former chief executive of Snowy Hydro, Paul Broad, said he was surprised by the scale of the rumoured costings.
"I'm a bit shocked. I don't know where this $12 billion comes from, that's news to me. Twelve months ago it was nothing like that," he told 2GB radio.
"That seems mad."
Mr Broad said it was a massive project facing many challenges and he was keenly awaiting the details from the review expected to be released on Thursday.
Environment Minister Tanya Plibersek said she had no additional information to add to the latest reporting on the project.
"Of course, we need to see a transition to renewable energy in Australia and there have been frustrating delays with Snowy 2.0," she told Sky News on Wednesday.
She said the former coalition government did not have a good track record when it came to delivering large projects, citing the NBN rollout and the Murray-Darling Basin plan as two examples.
Snowy Hydro 2.0 will connect two dams in southern NSW via almost 30km of tunnels and a new underground power station.
The project is intended to operate as a massive battery by using excess wind and solar energy to pump water uphill before releasing it during peak periods to provide power to the national electricity grid.
Snowy Hydro's new boss, Dennis Barnes, told a federal parliamentary hearing in May the project was making "positive progress" on a sinkhole issue that had interrupted tunnelling.
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