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The new restrictions could be introduced on Wednesday and remain in place until December 1, The Times said on Friday.
Johnson is expected to hold a news conference on Monday to announce the new measures, under which everything could be closed except essential shops and "educational settings," the newspaper said.
However, the new measures were still under discussion, and no final decision had been made, the Times added, citing a senior government source.
Cabinet Office officials did not immediately respond to a request for comment from Reuters.
The United Kingdom on Friday reported 24,405 new cases of Covid-19 and a further 274 deaths within 28 days of a positive test, according to government data.
It has now recorded more than 20,000 new coronavirus cases a day on average over the last week.
Covid-19 infections are rising so persistently in the United Kingdom that unless something can be done to reduce infections, the "reasonable worst case" scenario of 80,000 dead could be exceeded, scientists warned on Friday.
Currently, the government has a three-tier system of restrictions for local areas in England, with Level 3 the highest. Scotland, Wales and North Ireland run their own policies on fighting the pandemic.
In the third tier of restrictions, household mixing is banned, pubs and bars are ordered to remain closed, wedding receptions are not permitted, and travel to or from the area should be avoided.
The Times report added that the government is also considering tougher regional measures, known as Tier 4, but ministers are said to be in favour of a nationwide policy.