A government source told a newspaper that ministers are ready to introduce tougher measures if compliance with current restrictions does not improve by the weekend.
Some of the additional measures the ministers are discussing are said to be preventing two people from getting together outside to exercise and closing more businesses.
These closures would affect real estate agents, outside markets and stores offering click and collect services, it is claimed.
Updated government guidelines also suggest that moves may be temporarily banned.
A statement on the gov.uk website said: “It may become necessary to suspend all local or national moves for a short time to deal with the spread of the coronavirus. We will let you know if this should happen. ”
Another change that scientists have reportedly proposed is to increase the social distance rule from two meters to three meters, reports Mail Online.
Downing Street has said he would rather people follow existing rules than be forced to introduce new restrictions.
It comes as NHS health chiefs have warned that the peak of the current wave will not come until next month.
Chris Hopson, chief executive of NHS Providers, said MPs’ hospitals were facing increasing pressure despite nationwide lockdowns.
Giving evidence to the Health Committee, he said: “It now seems pretty clear that the rate of infection will not decrease as quickly as it did in the first phase, and it will drop more slowly due the increased transmissibility of the new strain.
“We were hoping for a sharp peak that would come shorter and shorter. So something for example where we saw the peak and started at the peak in mid January.
“Now it looks like the peak in demand from the NHS is actually in February.
“Now, if that’s true, it basically means there’s a higher level and a longer period of pressure on the NHS than we expected just a week ago. ”
NHS England data showed there were 32,070 Covid-19 patients in English hospitals as of 8 a.m. on Monday. The figure is up 20% from last week and 81% since Christmas Day.