Orkney could become a self-governing territory of Norway under new proposals being debated by councillors.
A motion is set to go before the authority's elected representatives on Tuesday to investigate "alternative forms of governance".
Council leader James Stockan said the islands were being let down by both the UK and Scottish governments.
He wants to explore what options are available to Orcadians, including looking at Crown Dependencies like the Channel Islands and overseas territories like the Falkland Islands.
Another possibility could be to do something similar to the Faroe Islands - which is a self-governing territory of Denmark.
Councillor Stockan told BBC Radio Scotland: "We are really struggling at the moment, we have to replace the whole ferry fleet which is older than the CalMac fleet.
"We are denied the things that other areas get like RET (Road Equivalent Tariff) for ferry fares.
"And the funding we get from the Scottish Government is significantly less per head than Shetland and the Western Isles to run the same services - we can't go on as we are."
He added: "We know that we have contributed for the last 40 years through north sea oil, and the dividend we get back isn't sufficient to keep us going," he said.
"We've got a unique opportunity right at the heart of all the wind projects round our waters."
Orkney was under Norwegian and Danish control until 1472 when they were handed to James III of Scotland after the Scandinavians welched on the dowry for his marriage to Margaret of Denmark.
Mr Stockan added: “We were part of the Norse kingdom for much longer than we were part of the United Kingdom.
“On the street in Orkney people come up and say to me, ‘when are we going to pay back the dowry, when are we going back to Norway?’
“There is a huge affinity and a huge, deep cultural relationship there.
“This is exactly the moment to explore what is possible.”
Orkney Islands Council previously voted in 2017 to look at whether the islands could have greater autonomy.
While they wanted to have a "stronger voice", they did not back full independence for Orkney.
Scottish Liberal Democrat MSP for Orkney Liam McArthur said: "As a Liberal Democrat, I’ve always believed in empowering individuals and communities to take decisions that best reflect their needs and circumstances.
"This is particularly important in our islands, where the effects of centralisation or a one size fits all approach by government can be most damaging, as we have seen over recent years.
“Nevertheless, recent history also highlights the dangers from putting up barriers between or creating divisions within communities.
"I am due to meet local councillors on Monday and will be interested to learn more about what is envisaged. There were similar proposals considered by OIC around the time of the last independence referendum and I am keen to understand how these would differ.
"Locally, I think islanders will also want to be reassured that this exercise won’t result in Council resources being taken away from the day to day running of services at a time when these are under real pressure.”
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