Whitehall officials and local authorities are reportedly considering alternative plans if the three-tier system in England has not made a difference by mid-November.
A potential plan B could include a "tier three-plus" or "tier four" which would see further restrictions brought in.
The measures under tier four - which has not been officially announced or decided but is reportedly being discussed - could include shutting restaurants and non-essential retail such as clothes shops, according to iNews.
The publication also reported that other options being discussed include the possibility of short-term local circuit breaker lockdowns in a bid to bring the R rate - the rate at which the virus is transmitted - below one.
Since October 12, England has been operating under a three-tier system of local restrictions which divides areas into different categories, labelled as medium, also known as Tier 1, high, also known as Tier 2, or very high risk, which is referred to as Tier 3.
Areas classed as medium risk, those in Tier 1, are subject to the same national measures that were commonplace across England earlier this year.
These include the 10pm curfew for pubs and restaurants and a ban on most gatherings of more than six people.
Areas categorised as high risk - Tier 2 - have restrictions on household mixing indoors while the rule of six continues to apply outdoors.
People must not meet socially with friends and family indoors in any setting unless they live with them or have formed a support bubble with them.
People living in Tier 3 areas such as Manchester and Liverpool are advised against overnight stays in other parts of the UK and should avoid travel where possible in and out of the area, unless it is for work, education or caring responsibilities.
In these areas, social mixing is banned both indoors and in private gardens, while pubs and bars must close unless they can operate as a restaurant.
The rule of six applies in some outdoor settings such as parks, public gardens and sports courts.
It comes as this week Nicola Sturgeon unveiled a new five-tier lockdown system for battling coronavirus in Scotland.
The First Minister said the levels, rising from 0 - 4, would avoid a "one-size fits all approach" for areas of the country with lower infection rates.
Level 4, the highest level, is closer to a full lockdown, Ms Sturgeon said, with non-essential shops forced to close and bans on indoor meet-ups.
According to official data, the UK has reported another 174 coronavirus deaths and 23,012 more cases in the latest 24-hour period.
The total number of infections in the country is 854,010, while the total number of fatalities is 44,745.
