Boris Johnson is expected to set out his plan - including details of how families can see different households at Christmas - to MPs on Monday.
More areas are set to be placed into the higher tiers to keep the virus under control, No 10 said.
And some tiers will be strengthened to safeguard lockdown progress.
It is not yet clear exactly how restrictions could change. Full details of the so-called "Covid winter plan" are expected on Monday, after cabinet discussions on Sunday.
Some local measures will be the same as those in the previous three tier system, used in England to tackle the spread of coronavirus up until the current lockdown began.