Pacific Aluminium wants the refinery to convert from heavy fuel oil to gas to reduce massive electricity costs, that contributed to the heaviest losses of its aluminium assets last year.
However that will require a $900 million pipeline and the gas supplies are yet to be secured, despite the NT having large potential for new gas production.
A new 600km pipeline to an energy-intensive refinery in remote Arnhem Land would provide a large boost to gas demand in the NT.
How the pipeline would be paid for has not been agreed on while NT gas producers Santos and Eni have refused to guarantee the $1 billion of supply from their offshore projects, with the potential to attract higher prices internationally.
Pacific Aluminium says it will decide what to do about Gove after completing a review this month, after it had set a deadline for a gas supply deal in December.
"They are highly complicated, contentious, potentially very risky negotiations," she told reporters.
"Negotiations have slowed but they can't be hurried because of the critical nature of getting this right for all Territorians."
"That (the end of December) was the deadline that Pacific Aluminium has defined. I am not sure if that is the deadline shared by the other players."
Pacific Aluminium said it was also considering the option of increasing bauxite exports in parallel with continued operation of the refinery.
"The other option being considered by the review is a suspension of refinery operations until economic conditions improve," it said in a statement.
Tensions are high over global petroleum companies that are exploiting Australia's natural gas resources with the aim of exporting liquefied natural gas (LNG) overseas to attract higher prices than domestic businesses can afford.
Aluminium producers are highly sensitive to power costs because it their biggest cost input, with Victoria's aluminium smelters the biggest energy users in the state.
Western Australia's government sets aside gas for domestic use but other states do not.
"It is only fair and reasonable domestic customers have opportunity to access cheap power in my view," Mr Wendt said.
"You can factor in the disadvantages Australian miners have compared to overseas players ... at a time when commodity prices are lower you have a high dollar, labour costs and higher energy costs so longer term the viability of the (Gove) operation has to be called in to question."