She urged the Home Office to help find “practical, deliverable, and evidence-based” solutions.
Powers over immigration are reserved to Westminster.
Scotland’s rural areas have experienced population decline over a number of years.
In 2019, their share of the working age population was between six and seven per cent below the Scottish average.
The Scottish visa plan would allow migrants to live and work in Scotland under separate eligibility criteria. For example, there would be no salary threshold.
Other models being explored by SNP ministers include relaxing the conditions attached to the skilled worker route in the UK immigration system.
A third option would be based on a scheme in Atlantic Canada that seeks to encourage economic development in order to retain young, native-born Canadians and attract migrants.
Ms Gougeon said: “The Scottish Government is already taking steps to address rural depopulation, through our population programme, the development of the islands bonds and our economic transformation strategy.
“We need to deal with a legacy of outward migration and depopulation, much of which pre-dates the establishment of the Scottish Parliament.
“This legacy and specifically its demographic impact means that we cannot just rely on retention of the existing population but we need to attract new people, families and those of working age who can help to grow and sustain our communities.
“We call upon the Home Office to work collaboratively with the Scottish Government to find practical, deliverable, and evidence based migration solutions that can meet the needs of our rural communities now and in the future.”
In a letter to UK migration minister Kevin Foster, Ms Gougeon said the Scottish Government will work with councils and business partners to develop proposals for a rural migration pilot scheme.
She said: “Once this work is completed, I would appreciate the opportunity to meet with you to discuss the outcomes and next steps.”