Some 3.6 million EU nationals are estimated to be living there
It is reported all European Union nationals living in the UK will be allowed to stay after Britain leaves the European Union.
The Daily Telegraph says the British Home Office has worked out that five in six of such migrants could not legally be deported.
Some 3.6 million EU nationals are estimated to be living in the UK - and it is thought more than 80% of them will have permanent residency rights by the time they leave.
The paper says the remainder of more than 600,000 people will be offered an amnesty.
Once an EU citizen has been in Britain for more than five years, they are given permanent residency rights.
It comes as German Chancellor Angela Merkel has stressed that Britain cannot have access to the EU's internal market after Brexit if it limits immigration from the bloc.
She said that giving Britain full access to free trade across Europe's border but allowing it to restrict the movement of people would lead to a free-for-all.
"If we don't say that full access to the internal market is linked to full acceptance of the four fundamental freedoms, a process will spread in Europe in which everyone does what they want," she said.
She also told a group of German businesspeople that upholding the EU's "fundamental freedoms," including free movement of EU citizens, remained essential.
British Prime Minister Theresa May has said she plans to formally trigger EU exit talks by the end of March.
While the Irish government will host an ill-island forum on Brexit next month.