Discovery also runs the free-to-air channels HGTV and Choice under the Discovery Media Sales arm.
A spokesperson from Discovery confirmed changes are underway.
"We are working to determine the structure, skills and capabilities needed to achieve our goals, as we integrate the Three and Top TV businesses into Discovery and create one organisation across Australia and New Zealand," the spokesperson said.
"Our people are our priority as we undergo this period of change."
Discovery would not be drawn on any further details regarding the scope of the changes or the exact number of roles involved.
Founded in 1985, Discovery is a multi-billion-dollar mass media company employing over 9000 people around the world. In addition to the Discovery Channel, it also owns and operates Animal Planet, the Food Network and a range of other media properties.
The television arm had long struggled under the ownership of MediaWorks, which retained its radio and outdoor properties when Discovery acquired the TV assets.
As part of that acquisition announcement, the company confirmed the New Zealand and Australian arms would be combined into one organisation spanning both countries.
The announcement said the combined business would be jointly led by general managers Glen Kyne and Rebecca Kent.
Discovery has until now cut no jobs in the local market, despite the impact of Covid-19.
However, the combination of the Australian and New Zealand arms suggested the possibility of duplicate roles being removed.
The Herald understands the current restructure will see staff across New Zealand and Australia compete for newly created roles within a reshaped business.
New Zealand isn't the only market where Discovery is making cuts.
A report in March suggested a British restructure in a bid to increase emphasis on streaming put around 10 per cent of roles in the region at risk.
Discovery-owned Eurosport also confirmed at the end of last year that it was set to make 59 redundancies at its Paris headquarters due to the effect of Covid-19 on the media sector.
Discovery shares recently traded at US$38,85, up significantly from around US$22 last year.