The possible measures being discussed include asking some hospitality businesses to close, or limiting the opening hours of some pubs and restaurants nationwide.
It comes as nearly two million people in north-east England are the latest to face local lockdown rules, which came into force on Friday.
The restrictions will ban people from meeting other households, and restaurants and pubs will have to shut at 22:00 BST.
New local lockdown rules are also set to be brought in for Lancashire - with the exception of Blackpool - the BBC understands.
However, Prime Minister Boris Johnson is understood to be deeply reluctant to order another national lockdown, where everyone would be asked to stay at home and businesses to close.
On Friday, parts of north-east England joined other areas across the UK in being under local lockdown rules
The restrictions for Lancashire, but not Blackpool, are expected to include a similar ban on households mixing and a requirement for hospitality businesses to close early
There are also local lockdown restrictions elsewhere in the UK - including Birmingham, Greater Manchester, Caerphilly, and the Belfast council area
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