The council said the scheme would provide an important source of income as it "prepares for a major fall in Government funding in the years ahead".
An initial study commissioned last year looked at four potential sites, two of which have since been ruled out as unsuitable for this kind of development.
Councillors have met this week to consider the report's findings and have now asked for further work to be carried out.
Other sites' potential as a wind farm location will be examined in more detail in discussion with the landowners.
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The next phase of work will involve drawing up detailed proposals for a large scale wind farm. Following this, a consultation on the draft proposals will take place to gather feedback from the public, local businesses and other organisations.
Council Leader James Stockan said the local authority expects a funding gap of £12 million over the next few years, which could "result in a range of cuts to services" unless it finds substantial new sources of income.
"A large scale wind farm has the potential to contribute significantly to the funding the Council needs to preserve and enhance the key services people in our community value and depend upon," she said.
A wind farm would require new grid links to the Scottish mainland, which would also support the further development of marine energy projects in our local waters.
"It would be remiss of us if we failed to fully assess a project of this kind, which could be of enormous benefit to our community.
"We are also well aware that wind farm developments attract a range of views – and we will listen to all views expressed during a comprehensive consultation exercise."
Councillors will discuss a further report on the next phase of work early next year.
(LM/MH)
