The military will carry out door-to-door testing for councils that want it in a bid to control the spread of the variant, The Times reports.
Andy Burnham, mayor of Greater Manchester, has reportedly backed the plan but demanded ministers send more vaccines to the region so a surge vaccination programme can be carried out over the next six-weeks.
Officials said the measures were not a local lockdown and people in the region were free to "get on with their lives", but should limit their travel plans if possible.
Speaking at a press conference, Burnham said: "This is guidance, it is advice to the public.