Johnson will reveal the full details of the much-anticipated approach in a statement to the House of Commons, or the lower house of the British parliament, on Monday, following criticism of his government for not keeping MPs properly informed of changes, according to the London-based Evening Standard newspaper.
The three tiers, known as Local COVID Alert Levels, are expected to be medium, high and very high.
Under a very high alert, pubs and bars would have to shut, but not restaurants.
The prime minister's chief strategic adviser, Edward Lister, said it is "very likely" that certain local areas will face "further restrictions" because of a "rising incidence" of COVID-19, the Sky News reported.
In a letter to MPs, Lister said the government would discuss "difficult choices" with local leaders.
At present, Downing Street is under pressure from regional leaders to consult them on lockdown measures.
After a meeting with government officials, leaders of West Yorkshire councils wrote a joint letter to Chancellor of the Exchequer Rishi Sunak saying, "We are concerned by rumours in the media that we might be pushed into Level Three of a new system set to be introduced, without any discussion or consultation, or without adequate economic measures put in place to support affected people and businesses."
Sunak has said the expansion of the Job Support Scheme will protect jobs and provide "reassurance and a safety net" for people and businesses across Britain in advance of a potentially "difficult winter".
In the regular daily update, another 15,166 coronavirus cases and a further 81 deaths were announced across Britain on Saturday.
Five of the 22 European regions with the highest coronavirus infection rates are in the north of England, the Sky News said.
To bring life back to normal, countries, such as Britain, China, Russia and the United States, are racing against time to develop coronavirus vaccines.