The First Minister has welcomed Jackie Baillie's intervention that a new Labour government would be open to talks about a Scottish visa which would give limited immigration powers to Holyrood.
John Swinney's comments came he highlighted problems, exacerbated by Brexit, faced by the social care sector in recruiting staff.
Care homes are facing staffing shortages with the issue meaning some patients in hospitals cannot be discharged because of insufficient places in the homes they would need to go to.
"We've undertaken lots of reform to integrate health and social care at local level," he told BBC Scotland's Sunday Show.
READ MORE: Jackie Baillie: Labour open to talks over Scottish visa
"We want to take further steps. We are working with partners to do that. But the key question is, we don't have enough working age population, which is the product of Brexit."
The BBC presenter Martin Geissler then drew attention to the Herald on Sunday's front page interview with Ms Baillie, the Scottish Labour deputy leader, where she suggested a Labour government would be open to discussions with Scottish ministers on a Scottish visa.
Mr Geissler asked if discussions were already underway.
Mr Swinney said: "Not yet. No. Nobody's approached us."
Pressed if he was surprised to see that headline, he replied: "I welcome it, because, if it's an indication of some of the practical steps that might come from intergovernmental relations with an incoming Labour Government then nobody will engage in that more strongly than me.
READ MORE: Baillie reveals how Labour plans to oust SNP in Holyrood
"But allow me to just be a wee bit doubtful about it, because that may be on the front page of a Scottish newspaper, but Keir Starmer and Yvette Cooper are on every UK television channel saying they're going to shut the door firmly on immigration."
He was pressed that that may be the case UK wide, but the party could have a separate Scottish policy.
Mr Swinney said: "Well, let's see what happens. I'll certainly engage in that, because we need a solution. If I take you back 20 years, the previous Labour Liberal executive brought forward a Fresh Talent Initiative, which we supported in opposition, because we recognised it was something that would benefit Scotland.
"I will work constructively to try to take forward measures like that, but just allow me to put the point forward that the Labour Party is taking a very, very hostile attitude towards migration and we would have to see how that would work out in practice."
During her interview with the Herald on Sunday Ms Baillie was asked about how a Labour government would respond to demands by the SNP for a Scottish visa and whether Labour would consider devolving any immigration powers to Holyrood.
She said: "So there would be dialogue and discussion but we need to recognise that growing home grown talent is really important.
"At the moment there are no plans for one, but I think if you have governments taking common sense approaches that an incoming Labour government would do, then dialogue will continue."
Former First Minister Nicola Sturgeon launched a plan for a Scottish visa pilot scheme in 2020 which would have allowed businesses and organisations struggling to recuit staff in remote and rural communities an exemption from UK immigration rules over hiring EU and other foreign nationals.
However, the Conservative Government blocked the scheme.
Ms Baillie's comments in an interview with the Herald on Sunday provoked a discussion among senior academics and policy analysts.
Dr Kirsty Hughes, a founder of the former think tank the Scottish Centre for European Affairs, said the move would be good for the Scottish economy.
She wrote on X, formerly Twitter: "If true that Labour would consider a Scottish visa, it's good news for Scottish economy. Scottish Government policy proposals on devolved migration powers have been serious and well made (helped not least by Scotland having very talented experts on this issue)."
Responding to Dr Hughes, Professor Anton Muscatelli, an economist and vice chancellor of the University of Glasgow, noted: "With regional devolution in England you could have regional visas across the UK it’s a good way to address UK labour short-term constraints on growth."
Peter Jackson, professor of global security at the University of Glasgow, wrote on X: "If this actually happens, and I confess that I remain sceptical, it would go some way toward giving a little substance to discourses around “levelling up” by recognising the specific economic situation in different parts of the UK."
With polls suggesting Labour will win next Thursday's general election and form the next UK government, the SNP's candidate for Inverness, Skye & West Ross-Shire Drew Hendry urged Labour to commit to delivering a Scottish visa in the party's first 100 days of government.
"It's welcome that Jackie Baillie acknowledges the specific needs of the labour market in Scotland - and there is no time to waste to support Scotland's bespoke needs.
"But this view is completely at odds with the Labour party's rhetoric in this campaign to date. If Labour is serious about this, they will commit to delivering a bespoke Scottish visa in their first 100 days in office.
"Migration is unashamedly a good thing for Scotland. We need inward migration to support our NHS, our social care sector and our world-class hospitality sector.
"So it's time for Labour's branch office in Scotland to show where their influence really sits - commit to deliver this crucial programme in the first 100 days, or admit they are telling Scotland one thing and doing the opposite when they get into power.
"The SNP is wholeheartedly committed to decisions about Scotland being made here in Scotland. If you value that principle, you have to vote for it - vote SNP on 4th July."
Scotland's population is set to fall and become older by 2045 presenting challenges about how to fund public services facing more demand with fewer people working to generate revenue through income tax.
It has been an issue of considerable concern for successive governments in Holyrood with both the SNP and Labour seeking to bring in policies to help address the issue.
Former Labour First Minister Jack McConnell launched the Fresh Talent Initiative in February 2024 saying he was doing to as a way of countering the "biggest challenge facing Scotland" of its falling population.
The scheme allowed overseas students from non EU countries studying in Scotland to remain in the country to work for two years following graduation.
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