Ministers in England, Wales, Scotland and Northern Ireland had been discussing a framework to ease coronavirus restrictions over the festive period to allow families to meet.
Under the talks, it was agreed that three households will be allowed to meet indoors over five days between 23-27 December.
Each nation is also considering the lifting of travel restrictions and rules on overnight stays.
But any moves allowing more movement are being urged to be used sparingly because public health officials are worried Christmas get-togethers could cause a January spike in Covid cases.
Speaking ahead of the meeting of the UK government's emergency committee Cobra, Welsh First Minister Mark Drakeford said he was "very hopeful" of progress being made - but cautioned any extra freedoms would not be an instruction to do "risky things".
Scotland's First Minister Nicola Sturgeon also stressed any changes would be "temporary" and "limited" and the Scottish government would "continue to ask people to err on the side of caution".
She said that the "details" may differ "to reflect different circumstances in each nation", such as what the definition of a "household" might be.
Prime Minister Boris Johnson has acknowledged there would be risks of letting people meet over Christmas but said families should have the chance to reunite.
Transport Secretary Grant Shapps earlier said all four UK nations were moving "very close" to agreeing rules on festive gatherings.
But he said Christmas travellers should plan journeys carefully and prepare for restrictions on passenger numbers.
At a Downing Street news conference on Monday to outline a "Covid-19 winter plan", Mr Johnson admitted Christmas this year would be very different to normal.
"I can't say that Christmas will be normal this year, but in a period of adversity time spent with loved ones is even more precious for people of all faiths and none," he said.
"We all want some kind of Christmas; we need it; we certainly feel we deserve it.
"But this virus obviously is not going to grant a Christmas truce.”