Nicola Sturgeon unveiled the proposals, designed to start talks with the UK Government, on Monday - which would allow foreign nationals to apply for a specific Scottish visa.

Papers published alongside Ms Sturgeon's announcement showed five possible methods for the system to work, ranging from wholly controlled in Westminster to operated by the Scottish Government.

Nicola Sturgeon's Scottish immigration visa plan refused by UK government

Nicola Sturgeon unveiled the proposals, designed to start talks with the UK Government, on Monday - which would allow foreign nationals to apply for a specific Scottish visa.

The Home Office rejected the plans just hours after the announcement, saying "immigration will remain a reserved matter".

But the former Stirling MP, who lost his seat to the SNP's Alyn Smith in December, told the Times the plans were "really something worth looking at" before urging the UK Government to change how they treat the Scottish Government.

He continued: "I think the people of Scotland are fed up with its two governments shouting each other out.

"It is counterproductive for that to be the case in some areas. The way to deal with the Scottish nationalists is to engage, not to be hostile."

Ms Sturgeon said that Scotland would need to increase inward migration in the coming years to stave off the decline of the working age population after Brexit.

SNP MSP Tom Arthur said: "Even people in the Tory party can see that the UK government's out of hand dismissal of our serious, sensible proposals is ridiculous.

"Without new powers Scotland faces serious demographic problems that could harm our ability to fund the NHS. The UK government has a duty to treat this issue with the gravity it deserves.

"If the candidates for Scottish Tory leader want to show that they plan to be anything more than Boris Johnson's mouthpiece, they should join business groups and get behind our plans for a Scottish visa."

Scottish visa proposals really worth looking at, says former Tory MP