The reports came as latest figures from HM Treasury showed that 8.4 million workers were included in the government’s furlough scheme, with claims rising to £15bn.
Treasury data also showed that the scheme for self-employed workers has now seen 2.3 million claims worth £6.8bn.
According to the reports, chancellor Rishi Sunak is thought to be poised to announce a cut-off date of the end of July after which companies will not be able to add staff to the Coronavirus Job Retention scheme.
Sunak is also likely to provide details about how employers will be expected to share the costs of the scheme, with the expectation that Treasury will continue to pay more than half the costs between August and October.
Firms may have to start paying about 20% of furloughed workers’ wages, plus National Insurance contributions. All firms using the Coronavirus Job Retention scheme will be required to make the payments, even if they remain closed.
However, the announcement is also likely to include a rule change which allows businesses to bring back staff part-time.
Under the government’s Coronavirus Job Retention Scheme, employers can keep staff on their payroll even if they can’t work because of coronavirus, with the Government paying 80% of their salary, up to a monthly maximum of £2,500.
The scheme opened on 20 April with almost a quarter of UK workers furloughed by their employers within the first two weeks of the scheme’s launch.
The scheme was initially due to end on 31 May but was later extended until the end of June. It was then extended by an additional four months until the end of October, although funding will be reduced from July.
The Office for Budget Responsibility says the scheme could cost up to £80bn.