A cross-party group of MPs has called on the UK government to "seriously consider" handing greater powers over immigration to Scotland.
The All Party Parliamentary Group on Social Integration said a commission should be set up to examine how a devolved immigration system might work.
It said the current system had "led to friction" between the UK and Scottish governments.
But it acknowledged there would be major challenges to overcome.
Immigration policy is currently the sole responsibility of Westminster, although the "shortage occupation list" allows Scottish businesses to offer particular jobs to non-EU nationals without first advertising them domestically.
The Home Office said it was not planning to introduce local immigration visa arrangements, but insisted its priority was to build an immigration system that worked for everyone in the UK.
In its report, the parliamentary group said the UK government should aim to encourage people to move to areas of the country which required higher levels of immigration or did not currently attract a great many immigrants.
This included Scotland, where the Scottish government and local authorities believe that increasing immigration will help to offset the country's declining and ageing population.
Giving greater control over immigration to Holyrood has been a key demand of Scottish First Minister Nicola Sturgeon in the wake of the Brexit vote.
The All Party Parliamentary Group (APPG) report agreed that the UK's current point-based system is "generally unresponsive to demographic, economic, and cultural differences between our constituent nations and regions".
It added: "This has led to friction between the Scottish and UK governments, as the former's aim of increasing immigration (in order to grow its labour force) has come into conflict with the Home Office's commitment to cut net immigration."
The report said Scottish councils had done a "significant amount of work" to attract more immigrants but that these efforts could be "undermined by a nationally-driven reduction in the number of immigrants arriving in the UK".
It pointed to Canada as an example of a country which had introduced a regionalised immigration system.
How does the Canadian immigration system work?
- All 10 Canadian provincial governments are able to set region-specific requirements for immigrants
- This allows them to address labour shortages in certain fields and industries within their regions and to enforce place-specific cultural criteria
- Immigrants are required to live within the region which approves their visa until they become eligible to apply for Canadian citizenship
- The Canadian federal government has also attempted to create incentives for immigrants to move to new areas
- Regions and towns in provinces including British Columbia have been supported to design and launch "Welcoming Communities" initiatives
- These federally-funded schemes aim to attract immigrants to live and work in their areas through investment in infrastructure improvements and initiatives promoting positive attitudes towards cultural diversity
The report added: "The APPG calls on the government to seriously consider devolving a degree of control over immigration policy powers to the constituent nations and regions of the UK so as to boost levels of integration.
"The government should appoint an independent commission to explore how a devolved or regionally-led immigration system might work."
It suggested that the commission could examine questions such as:
- Whether the shortage occupation list which is already devolved to Scotland could be extended to other areas of the UK, including Wales, Northern Ireland and London
- Whether these powers could be strengthened to enable the nations and regions of the UK to develop immigrant criteria to reflect their specific demographic and cultural conditions
- Whether the UK government might copy the Canada-Quebec Accord, which sees immigration substantially devolved to the provincial government of Quebec
The report said: "Devolving substantial immigration policy powers to the UK's nations and regions would almost certainly involve significant challenges, but might be achieved through the introduction of region (and potentially sector) specific visas.
"Quotas for the dissemination of these visas could be agreed by devolved administrations, city regions, and other democratic forums."
It said shaping immigration policies to address national and regional economic and cultural needs might instil confidence among members of the public that the immigration system works for their area.
And it said enabling nations and regions to set regional immigration quotas would give politicians the incentive to actively make the case for immigration in their area.
The APPG is chaired by Labour MP Chuka Umunna, and has members from Labour, the Conservatives and SNP, as well as the SDLP and Democratic Unionists.
Its report also said migrants should be expected to learn English before coming to the UK, or attend language classes when they arrive, as integration was a "two-way street".
Responding to the report, the Home Office said it was not planning to introduce local visa arrangements, but the department said it had made funding available for more English lessons.
A UK government spokesman said: "Our country has long been home to lots of different cultures and communities, but all of us have to be part of one society - British society."
He added: "We must also recognise that uncontrolled, mass immigration makes it difficult to maintain social cohesion and puts pressure on public services.
"Our priority is to build an immigration system that works for everyone in the UK and delivers the control we need."
The Scottish government said the UK's approach to immigration was "driven by a desire to reduce the numbers of incoming migrants and does not recognise Scotland's specific circumstances or serve our economic or societal interests".
A spokesman added: "It is widely regarded that Scotland's population needs are different to the rest of the UK's and we have consistently called on the UK government to consider a more flexible approach, for example through the reintroduction of a post-study work route and most recently in Scotland's Place in Europe, the paper published last month on options to keep Scotland in the Single Market.
"These are not just the views of the Scottish government, but have the support of stakeholders in Higher Education and business, and were also highlighted in the Scottish Affairs Committee's recent report on demography in Scotland."