The Met Office has said that temperatures are expected to plunge moving towards the end of January, but it cannot say if the country will be hit by a whiteout.
But the forecasters said that by the end of the month the temperatures are expected to drop and conditions to become more "wintery".
The average national temperature for January is 3.5C.
A Met Office spokesman said: "Next week there will be colder spells and there could be a little bit of winteriness in the north, but nothing too exceptional for this time of year.
"As we head towards the later part of January it will turn colder, but there's still a lot of uncertainty in that forecast about where any snow will fall.
"The week beginning Monday, January 21, there is a stronger signal of it getting colder, that would increase the risk of snow across the UK."
Forecasters warned earlier this week that the same weather patterns which sparked the Beast from the East - and brought freezing temperatures and heavy snow last winter - could return this year.
The Met Office said sudden stratospheric warming had appeared around Christmas, when there was a sharp increase in the temperature over a couple of days.
When this happens in the Arctic it can lead to a rush of cold air blowing eastwards across Europe a few weeks later, bringing much cooler temperatures to the continent.
The Met Office said this is what caused the Beast from the East early last year - an icy blast of freezing Siberian winds which brought freezing temperatures and heavy snow to much of the UK.
But a spokesman on Tuesday said that while Britain being hit by a new Beast from the East could not be ruled out, the forecast so far suggests the country will see stable weather conditions.
He said: "There have been some parts of Europe that have experienced quite significant cold, heavier-than-average snow in countries like Austria and in northern and central Europe.
"We are looking at the next week or so, but we could see a change after that. But there is nothing in the next week or so that could indicate any change like the Beast from the East."