The company opened its proposals for public consultation last week, and is now due to move into the planning and consent phase of the project, including environmental impact assessments.
The proposed facilities at Vementry would include 12 salmon pens with a circumference of 120 metres, in addition to a feed barge moored alongside.
Cooke previously developed its first offshore fish farm in Orkney, at its Skelwick Skerry site, which is notes is one of the most exposed locations in Scotland.
The new Shetland-based farm, it says, would be located in an even more exposed environment, building on the know-how gained by operating the Orkney site.
According to Cooke, "the proposed site is a high energy environment which will have optimal conditions for rearing strong and healthy fish whilst minimsing potential effects on the local environment."
As detailed in proposals published on Cooke's website, the farm would be serviced on a daily basis from its existing shorebase at Aith, with the intention of creating five highly skilled full-time jobs in the local area.
Cooke is currently one of the largest employers in Shetland. According to the company, in addition to job creation, the local community will benefit from continued investment as the company's operations grow in the region.
"Since 2017 we have spent £260,000 in local communities in Shetland through our Community Benefit Fund and with new developments we plan to invest in the local communities we work within," the company said.