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These countries include South America, Portugal, Cape Verde and South Africa, the report added.
Separately, Johnson has rejected calls by interior minister Priti Patel for a temporary closure of borders, the newspaper reported, adding Patel had pushed for a travel ban to stop potentially vaccine resistant strains of coronavirus being imported into the country.
Johnson has said he was looking at the option of introducing quarantine hotels for those coming to Britain to prevent the risk of "vaccine-busting" new Covid-19 variants entering the country.
The bosses of airlines including British Airways, Virgin Atlantic and easyJet criticised on Tuesday a possible plan for mandatory quarantine in hotels for some or all arrivals to Britain and called for a support package.
Britain has suffered a sharp rise in infections and deaths in the new year, fuelled partly by a new more highly contagious variant of the virus first identified in southeast England.
The death toll in Britain from the coronavirus pandemic passed 100,000 people on Tuesday.