The Northern Territory chief minister is coming under scrutiny over her ownership of shares in gas company Woodside, with one federal senator wanting it to be examined by an ongoing inquiry.

properly declared the holdings each year and that she has acted in line with financial disclosure rules for NT politicians.

Since the row emerged earlier this week, Australian Capital Territory independent senator David Pocock has raised the issue in federal parliament, saying he wants a federal senate inquiry into the Middle Arm Sustainable Development Precinct to scrutinise her shareholding.

"This is the Labor chief minister who's been pushing fracking in the NT and pushing for the development of something that is not in line with the NT being habitable," he said on Tuesday.

"We know from the latest IPCC report that, if we continue down this road, large swathes of the NT will be uninhabitable.

"But she's pushing it, and today we learn that, allegedly, she actually has shares in one of these companies."

Senator David Pocock wants the share portfolio examined in a senate inquiry.(ABC News: Matt Roberts)

Senator Pocock told ABC Radio Darwin scrutiny of the Woodside shares was well within the scope of the federal inquiry, given the federal government was giving $1.5 billion to the Middle Arm precinct.

The Northern Territory Greens have also described Ms Fyles's Woodside shares as a "questionable asset", and in a statement called on her to publicly reveal the number of shares she owned and their value.

It follows the NT government approving commercial gas extraction in the Beetaloo Basin in May this year, a step opposed by environmental groups and dozens of scientists. 

The development of the Middle Arm Sustainable Development Precinct has also attracted criticism, with environmentalists warning it amounted to an expansion of the gas industry.

Ms Fyles has repeatedly said on-shore fracking in the NT would be subject to strict regulation and that Middle Arm represented an opportunity to help transition between fossil fuels and renewables.

Chief minister defends Woodside shares

In a statement to the ABC, a Woodside spokesperson said it had no involvement in the Middle Arm Sustainable Development Precinct.

Speaking on Monday, Ms Fyles denied any wrongdoing and said members of the NT's Legislative Assembly were mandated to declare any potential financial conflicts.

"I own my own home, we have a number of situations — we declare all of that so that people can then ascertain what potential conflicts we have," she said.

"These have been declared for over a decade, the media seem to have picked up on it recently.

"I accept any criticism but from my perspective everything that needs to be declared is, and that can be from my membership at my local sports club through to my own home."

On Monday, NT Opposition Leader Lia Finocchiaro said it was "really important governments act openly and transparently", and warned the perception of a conflict of interest "puts a cloud" over attracting investment.

She said the chief minister needed to answer questions about whether her ownership of shares in certain companies had any impact on her decision-making.