The government’s medical adviser on Covid, Susan Hopkins, said they were working on a plan and wanted Christmas to be “as close to normal as possible”.
BBC health correspondent Nick Triggle said any rule change would be for a limited time, maybe just a few days.
Cabinet minister Alok Sharma said it was too early for “conclusions” but he wanted to see his family for Christmas.
It comes after the Sun reported that families may be able to mix indoors for five days from Christmas Eve.
All four UK nations – England, Scotland, Wales and Northern Ireland – are trying to work out a common approach to Christmas so families spread across the UK can still meet up.
Our correspondent said any final decisions would not be made for a few weeks while health chiefs wait to see whether cases have started to come down during the lockdown in England.
But, he said, the advice was likely to urge families not to hold big gatherings and to travel by car, rather than public transport.
Scientific advice indicates that for every day that measures are relaxed, five days of tighter restrictions would be needed.
The government has recorded another 19,609 Covid cases in the UK and 529 more deaths within 28 days of a positive test.
England is expected to come out of its second national lockdown on 2 December and return to the tier system of localised restrictions, with household mixing banned indoors in the top two tiers.
The United States has recorded a quarter-million Covid-19 deaths, the latest NBC News numbers showed Wednesday, and the death rate has been accelerating in recent weeks as cases have been surging across the country.
The 250,000th death was logged Wednesday morning, the data revealed.
In the last four weeks, there has been a 42 per cent increase in the number of fatalities, from a weekly average of 821 per day in early October to last week’s average of 1,167 fatalities per day, according to an NBC News analysis of the available data.
And, a year after the first Covid-19 infection was reported in China, people were dying in America at a pace not seen since mid-August, the analysis showed.
The Department of Health In Ireland has reported 12 additional deaths related to Covid-19, bringing the total number of deaths here to 2,006.
A further 379 new cases of the virus have been confirmed. Seven cases have been denotified which means there have been a total of 69,058 confirmed cases of Covid-19 in Ireland.