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.
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 and a government source said there could be "light touch migration" rules for EU nationals as part of any wider Brexit trade deal.
The government does not call this "preferential" treatment because a similar arrangement could be struck with, for example, the US as part of a UK-US trade deal.
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