EU nationals arriving in the UK before the end of next year could be permitted to stay for three years in the event of the UK leaving the EU without a deal.
The government is expected to announce later that a temporary Leave to Remain scheme would replace free movement.
This would allow EU nationals who arrive before the end of 2020 to stay until December 2023.
The government had hoped to end the free movement of EU nationals under a no-deal Brexit.
Free movement of EU citizens will not automatically end as a result of a no-deal Brexit, because EU law will continue to apply until its legal foundation is repealed.
Last month, the UK government announced EU free movement rules would end immediately if there was a no-deal Brexit on 31 October.
This would have affected the rights of any EU citizens arriving in the UK from November onwards.
At the time, Liberal Democrat home affairs spokesman Sir Ed Davey accused the government of being “irresponsible and reckless”.
And the 3million group, which campaigns for the rights of EU citizens living in the UK, said it could mean “millions of lawful citizens” would have their legal status removed “overnight”.
However, it emerged at the weekend that the plan had been dropped because the government could have been challenged in the courts.
Migration experts had said the UK could not end freedom of movement from the EU on Brexit day because it has no system to work out who is legally in the country.
The EU settlement scheme aims to register EU nationals in the UK, but there is no obligation for all of them to take part.
As of July, only a third of the estimated 3.3 million UK-based EU citizens had applied, leaving more than two million unregistered.