The UK's Brexit minister has urged the EU's Michel Barnier to have a reciprocal agreement guaranteeing citizens' rights in the event of a No Deal Brexit.
In a letter, Brexit Secretary Stephen Barclay said this would be "far superior" to the current approach of negotiating with 27 other countries individually.
But EU chief Michel Barnier warned ring-fencing people's rights is "far from straightforward".
Although he promised "no British national will be left in the dark," Barnier said agreeing a Brexit deal should remain the number one priority.
The EU's chief negotiator said that the provisions of the agreement are "part of an overall and comprehensive approach", in effect that there can be no cherry-picking of the deal, which is in any case "not open for renegotiation".
Barnier insists that all the citizens' rights provisions of the agreement, including the right to see cases adjudicated by the Court of Justice of the EU, and the Irish backstop, are interdependent and cannot be separated without treating some citizens unequally.
Departing prime minister Theresa May has said EU citizens in the UK will be able to stay even if there is no deal done.
The prospects of a no deal Brexit have significantly increased in recent weeks following the resignation of Theresa May, and the apparent death of the Withdrawal Agreement and political declaration on future relations which she negotiated with EU leaders.
Boris Johnson, who on Tuesday comfortably topped the second ballot of Conservative MPs in the leadership contest to succeed May, has promised to re-open talks with the EU and stated that the UK must be prepared to walk out of the EU without a deal.
In that scenario, those with a right to permanent residence - which is granted after they have lived in the UK for five years - should not see their rights affected.
There is uncertainty, though, about what no deal would mean for Britons living in France, Spain, Germany and elsewhere. The priority for most will be to register as residents, but the rules - including deadlines for paperwork - vary from country to country
About 1.3m UK citizens live in one of the other 27 EU member states, while the UK hosts about 3.2m EU nationals.