A review of lockdown measures will take place later this week after the hospital coronavirus death toll rose above 10,000.
Ministers have said they want to be sure the UK is past the peak of the outbreak before easing the restrictions, but 10 members of the cabinet are reportedly urging lockdown conditions to be eased amid concerns about the impact on the economy.
The Times quoted an unnamed minister as saying it was important not to do “more damage”, and measures could be eased after another three weeks.
Scientific advisers will meet on Tuesday ahead of the formal review of the strict physical distancing measures on Thursday, the deadline set out in law.
The chancellor, Rishi Sunak, who warned during his budget last month that the UK risks falling into recession as a result of disruption caused by coronavirus, has injected £14bn from the coronavirus emergency response fund into the NHS and local authorities.