The UK's four nations have backed plans to allow some household mixing "for a small number of days" over Christmas.
It comes as Prime Minister Boris Johnson is due to unveil on Monday a tougher three-tiered system for England - to be introduced at the end of the current lockdown on 2 December.
The 10pm closing time for pubs and restaurants could also be relaxed.
Work to finalise the arrangements for a UK-wide approach to restrictions this Christmas is ongoing.
It is said that one option that has been discussed is that three households could be allowed to meet up "over a number of days, maybe five days".
The Cabinet Office said ministers from England, Scotland, Wales and Northern Ireland had endorsed a "shared objective of facilitating some limited additional household bubbling for a small number of days".
But they have emphasised that the public will be advised to "remain cautious", and that "wherever possible people should avoid travelling and minimise social contact".
Discussions are continuing - including about travel arrangements - but it is hoped agreement on the joint approach can be reached this week. The Scottish government said "no agreement has been reached".
In respect of Northern Ireland, ministers have also "recognised that people will want to see family and friends across the island of Ireland, and this is the subject of discussions with the Irish government", the Cabinet Office said.
More areas are set to be placed into the higher tiers in England, with ministers to identify the which areas will be in which tier on Thursday.
Some local measures will be the same as those in the previous three-tier system, which was in place in England until the current lockdown began. But some tiers will be strengthened, according to Downing Street.
The PM will detail the strengthened tiered system in a statement to the House of Commons on Monday, but full details of Christmas plans are not expected until after the first ministers of Scotland, Wales and Northern Ireland have consulted their own cabinets.
There have been calls by a cross-party group of MPs and peers for the PM to guarantee that church services will go ahead this Christmas, as current lockdown restrictions forbid most religious services.
The government's Scientific Advisory Group for Emergencies (Sage) is expected to publish research saying the previous tiered restrictions in England were not strong enough.
But 70 Tory MPs have said they will not back the proposals without evidence.
In a letter to the prime minister, the recently-formed Covid Recovery Group (CRG) said it cannot support a tiered approach unless it sees evidence measures "will save more lives than they cost".
MPs are expected to vote on the new tier system in the days before it comes into force.
