Orkney Islands Council has agreed to allow Northern Oils to investigate whether the tanks, built inside a hill on the island of Hoy, can be used to store and supply marine gas oil.
Six tanks were tunnelled into the hillside above Lyness during the Second World War to give them protection from air raids.
They held up to 132 million litres (114,000 tonnes) of fuel oil for supply to British and Allied warships stationed in Scapa Flow.
Michael Morrison, business development manager with the council's Orkney Marine Services, said it was a tremendous feat of engineering and, 60 years on, the tanks appeared to be in remarkably good condition.
"We've been in discussion with Northern Oils about the tanks' potential as a base for the storage and distribution of marine gas oil for modern day shipping.
"It's an exciting concept we were keen to explore. The proposal is for the company to spend up to year on detailed investigations into the viability of the project, we look forward to the outcome," he said.
David Wood, managing director of Lintmill-based Northern Oils, said Orkney was an ideal location for the company to establish a fuel distribution hub supplying customers in the UK, Ireland, Scandinavia, Iceland and the Faroe Islands.
"Over the coming months we will investigate the logistics of giving these wartime assets a new lease of life."