A Scottish visa could emulate current freedom of movement from Europe and be opened up to further afield, Scotland's Europe and Migration Minister has said.
Ben Macpherson said the additional immigration route proposed for Scotland could end planned UK Government caps and charges after Brexit.
He said there is increasing support from business on the issue due to "alarm" over UK Government immigration plans.
Discussions with the UK Government on the issue are "making traction", he said.
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The UK Government proposes one system for the whole of the UK that would end freedom of movement, allowing visas for skilled workers sponsored by an employer and meeting a minimum salary - with a recommendation this is set at £30,000.
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Its immigration white paper includes proposals for a 12-month visa "transitional" route, which would be developed for short-term workers with no skill requirement, restricted to migrants from certain countries.
Speaking on a visit to the Royal Highland Show in Edinburgh, Mr Macpherson said the current proposal is for a Scottish visa within a UK framework, offering an additional route into Scotland, where successful applicants would live and work.
He said it would be in conjunction with the UK Government - as the Border Force would be reserved - but the rules and criteria would be set by the Scottish Parliament to "give us the best visa to fit the needs of Scotland".
"We could decide to have a lower salary threshold, we could decide to have no salary threshold, we could decide not to have an immigration skills charge, we could decide if we wanted to emulate freedom of movement from the European Economic Area (EEA)," he said.
"The capacity and opportunity of designing the rules and criteria of the Scottish visa could allow us to expand it beyond the EU but in the first instance, because we are of course facing the end of freedom of movement from the EEA, this is of particular interest to those who would want to continue to attract people from the rest of Europe."
He said no cap on EEA migrants is possible, adding: "Currently the UK Government has a cap on numbers but that hasn't worked and actually we need to grow our population in Scotland so these are matters that we could decide in terms of the rules and the criteria that we would set here in Scotland."
Mr Macpherson added: "What is clear is that ending freedom of movement from the EEA as is proposed through Brexit and the implementation of the UK Government's white paper on immigration will have a very negative effect on Scotland and that has been shown through the independent analysis of the expert advisory group."
In response to questions from public at the Royal Highland Show on the discussions with the UK Government on the Scottish visa, he said progress has been "slow" but believes "we are making traction".
Scottish Conservative chief whip Maurice Golden said: "Ben Macpherson's only motivation for saying these things is to agitate for a second independence referendum.
"His claim about differing opinions on immigration have been repeatedly disproved.
"He is only saying that in the hope of driving a wedge between Scotland and England.
"The SNP would be better served trying to improve its miserable domestic record than pontificating on other matters."