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Queenstown company RealNZ has begun a feasibility study into alternatives ways of generating the steam that drives the vessel, which turns 109 today.
Chief executive Stephen England-Hall said the ship's original boilers would soon need replacing.
It would be a "major and invasive piece of work" requiring the vessel to be out of the water for an extended time.
"That would be the obvious time to implement a carbon-neutral or carbon-zero solution," Mr England-Hall said.
"We will essentially look for a new source of heat to generate steam that replaces the coal."
Carbon-neutral options were wood pellets or bio-diesel fuel, while carbon-zero options were renewable hydrogen fuel, battery-electric or fully-electric.
The Earnslaw is the oldest coal-fired passenger-carrying steamship in the southern hemisphere.
It carries passengers across Lake Wakatipu from Queenstown to the Colonel's Homestead and Walter Peak High Country Farm.