The current lockdown could be lifted from March after the Government approved a three-point plan.
Cabinet has reportedly agreed a strategy for lifting lockdown measures, the Sunday Times reports.
The paper also says that all arrivals to the UK may be forced to quarantine at a hotel in even tougher measures being considered to stop new variants entering the country.
Ministers are reportedly considering an even tougher crackdown at the borders, the Mirror reports.
Officials are said to have been told to prepare for the creation of quarantine hotels for those arriving in Britain and to use GPS and facial-recognition technology to check that people are staying in isolation.
The discussions come after Boris Johnson scrapped all isolation-free travel corridors on Friday.
The Prime Minister said the measure would protect the UK from new Covid variants anywhere in the world, with the UK having banned flights from South America and Portugal earlier in the week.
Meanwhile, the key barometers to lifting lockdown in March - a few weeks after the Government hopes all over-70s will have had the first dose of the vaccine - have been thrashed out by Cabinet, the Sunday Times reports.
Ministers will reportedly begin drawing up a timetable for the end of lockdown at the end of this week once they see the first evidence of the latest national lockdown's effects.
Areas will be put into lower tiers once their death rate has fallen, the number of hospital admissions drops and some in the 50- to 70-year-old age range are vaccinated, as this age group spends the most time in hospital with the virus.
Meanwhile, Health Secretary Matt Hancock said the UK is "nearly on the home straight" as 324,000 doses of coronavirus vaccines were administered in the space of 24 hours.
More than 3.5 million people in the UK have now received their first dose of a vaccine, Prime Minister Boris Johnson said, as he hailed those helping the "fantastic national effort".
Two vaccines have been rolled out in the UK, with a third - developed by Moderna - also approved for use.
Mr Hancock, writing in the Sunday Express, said: "We can see the way out of this pandemic. We are nearly on the home straight.
"After months of detailed preparations, rigorous scientific scrutiny and an extraordinary amount of patience, we are rolling out two highly effective vaccines, with a third coming in spring and others progressing through clinical trials.
"We're rolling it out to as many vulnerable people as possible and we expect tens of millions of people to be vaccinated by the spring."
Ten further mass vaccination centres will open in England this week with more than a million over-80s invited to receive their coronavirus jab.
Blackburn Cathedral, St Helens rugby ground, Norwich Food Court and a park-and-ride outside York are among the new locations where large-scale vaccination will take place from Monday.
NHS England said they joined the seven existing mass vaccination sites across the country, alongside a thousand GP-led surgeries and more than 250 hospitals already providing jabs.
It comes as the Government prepares to suspend all quarantine-free travel into the UK on Monday in a bid to keep out new coronavirus variants.
The new policy means arrivals from every destination will need to self-isolate for 10 days, or receive a negative result from a coronavirus test taken at least five days after they enter the UK.
His plea came as another 1,295 deaths in the UK were reported on Saturday, the third-highest daily total since the pandemic began, but the lowest number of lab-confirmed cases this year was reported - 41,346.
The figures will be seen as a sign that infections may be levelling off or falling as a result of the lockdown measures, though scientists believe the peak in deaths will come later.