People from the EU should face the same immigration rules as those from elsewhere, once the UK has completely left the bloc, the cabinet has agreed.
The agreement in principle follows a recommendation of the independent Migration Advisory Committee (MAC), which was also backed by Labour.
The cabinet unanimously supported a system based on skills rather than nationality, a source told the BBC.
But some fear that a bar on low-skilled EU migrants may damage business.
The prime minister has repeatedly vowed to end unlimited immigration from Europe after Brexit.
BBC political editor Laura Kuenssberg said: “Ending freedom of movement as it stands has become a rhetorical non-negotiable for Theresa May.”
The cabinet agreement came after a presentation from the MAC chairman, Prof Alan Manning, at a lengthy meeting on Monday.
According to one source, the principle was agreed that the UK would not show bias towards immigrants from any one part of the world over another when granting access to work.
However, one cabinet source told the BBC the agreement did not constitute a firm decision.
What is the Migration Advisory Committee?
- An independent public body, the MAC was commissioned by the Home Office to advise the government on migration issues
- The panel is made up of Prof Manning and five other independent economists, along with a Home Office representative
- It reports on issues including the impacts of immigration, the limits on immigration under the points-based system, and skills shortages within occupations
The EU’s principle of freedom of movement currently allows people from the European Economic Area – all EU countries, as well as Norway, Iceland and Liechtenstein – plus Switzerland, to travel and work within the area without visas, regardless of skills.
The UK is due to withdraw from the European Union on 29 March next year, although an “implementation period” lasting until 31 December 2020 has been agreed.
In that transition period, EU citizens arriving in the UK will enjoy the same rights and guarantees as those who arrive beforehand. The same will apply to UK expats on the continent.
It remains unclear what would happen in the event of a “no-deal” Brexit.
Under the current immigration system, most non-EU workers are rated on whether their skills are needed by the UK economy.
Last week, the MAC called for the annual limit on the number of high-skilled workers from outside the EU granted permission to work to be scrapped.
Currently set at 20,700 a year, the cap – imposed by Mrs May when at the Home Office – has resulted in thousands of IT specialists and NHS candidates being denied visas.
A change in the rules for NHS workers was announced in June after pressure from health bosses.
Lobby groups such as the Campaign for Science and Engineering have argued that job offers in other areas, such as science and engineering, should also be exempt from the rules.
Labour has proposed to scrap net migration targets altogether and introduce a “flexible work visa” available to “all those we need to come here” who could prove bona fide skills, such as doctors, scientists, or care workers.
And Home Secretary Sajid Javid has previously said he was taking a “fresh look” at the Tier 2 cap.
Some business groups, particularly in industries such as agriculture and hospitality, have warned that any future arrangement barring low-skilled migrants could cause huge disruption.
Last month, the CBI warned the UK “risked having too few people to run the health service, pick food crops or deliver products to stores around the country” if it got the overhaul wrong.
The PM could make an announcement about new immigration rules at next week’s Conservative Party conference, it has been suggested.