An all-party group has called on the UK government to consider devolving some immigration control.
That could involve Wales being able to set its own visas and migration quotas. And the group chairman said immigrants should have to learn English or Welsh.
The UK government said different rules for different areas would cause difficulties for employers.
Currently, there is no separate Welsh immigration policy.
A number of recommendations have made by the All Party Parliamentary Group on Social Integration (APPGSI) report on how the UK's immigration system could promote better integration.
It said speaking English was "the key to full participation in our society and economy".
Group chairman Chuka Umunna MP said he wanted Wales to have a bigger say in developing immigration policies.
"This is a really hot topic, it's become very toxic, very polarised and we want to build a consensus on what a new system could look like," he told BBC Radio Wales' Good Morning Wales programme.
When asked if immigrants could learn Welsh if living and working in Wales as an alternative to English, he said: "Absolutely. Why not?", adding that people could not fully integrate in society if they could not speak the language.
David Davies, Conservative MP for Monmouth, called it a "ludicrous idea".
"People will just go to whichever nation... is offering the easiest visas and move to where they want to move to," he told BBC Wales.
"Once they've got a visa to go to Wales there will be nothing to stop them going to England or vice versa."
The MPs' report claims the UK's existing points-based immigration system is "generally unresponsive to demographic, economic and cultural differences between our constituent nations and regions".
"Shaping immigration criteria to address nation or region-specific economic and cultural needs might instil confidence among members of the public that the immigration system works for their area", the study said.
It added: "Enabling nations and regions to set regional immigration quotas would create new incentives for politicians to actively make the case for immigration in their area."
Devolution could involve the introduction of region-specific visas, with quotas for how many are issued.
Canada is given as an example, where all 10 provincial governments are allowed to set region-specific requirements for immigrants.
Immigrants are required to live in the region that approves their visa until they become eligible to apply for Canadian citizenship.
The province of Quebec is also able to set its own criteria for its visas and evaluate applications.
A small element of regional policy on immigration already exists in the UK, where Scotland has a list of occupations in addition to a UK-wide version where employers can advertise outside of the EU without first advertising domestically.
The UK government, the report said, should appoint an independent commission to explore how a devolved or regionally-led immigration system might work.
Questions for the commission could include extending existing powers for Scotland to Wales, Northern Ireland, London and the English metro regions, and whether the UK government might copy the Quebec model.
A Welsh Government spokesman said: "It is important that the needs of Wales are reflected in future migration policies and that people who settle here are supported to integrate into communities."
Plaid Cymru external affairs spokesman Steffan Lewis said: "Plaid Cymru has long advocated a Welsh visa system to boost our public services such as the NHS and support the private sector in attracting high-skilled workers from around the world.
"It is also of great regret that Westminster policies have damaged our reputation as a destination for international students.
"Student visas should be devolved and would benefit our universities and our economy."
A UK government spokeswoman said: "Applying different immigration rules to different parts of the United Kingdom will complicate the immigration system, harming its integrity and causing difficulties for employers who need the flexibility to deploy their staff to other parts of the UK."
She said the UK government was rolling out a Â£20m fund for English language provision and had made Â£140m available to councils to manage impacts on communities "caused by issues such as poor English language skills".
The spokeswoman 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."
Immigration rules tailored to the needs of Wales could build public confidence in the system, a group of MPs has said.