According to the Financial Times, Sunak is said to be considering a scheme whereby the Treasury and companies could share the cost of topping up part-time wages.
With the onset of tighter operating restrictions being imposed on the hospitality sector, calls for continued furlough support has increased in the past few weeks.
Earlier this month, trade body UKHospitality warned that at least 900,000 hospitality jobs are at risk unless Government offers a sector-specific package of employment support that helps businesses retain valuable workers.
The FT reports that a range of support measures are on the table, and although no decisions have been taken the Treasury is said to be looking at schemes in France, Germany and Spain that help businesses unable to bring back employees on a full time basis because of the ongoing crisis.
Sunak met Trades Union Congress leaders and the CBI employers’ group last week, and both have proposed new job support schemes.
The CBI has outlined a scheme, to be in place by 1 November, which would be available to all companies and last a year. It would involve a state subsidy if an employer was able to offer workers at least 50% of their normal hours.
The company would pick up the full wage bill for the hours worked by an employee. But for non-working hours the bill would be shared, with a third paid by the company, a third by the Treasury and a third foregone by the employee.
Under the CBI plan, companies could choose whether to participate in its proposed work subsidy scheme or take the £1,000 'job-retention bonus' offered by the Government to businesses that take back on to their payroll people currently furloughed.
The TUC's proposal, meanwhile, would similarly apply to employees who are still working 'for a minimum proportion of their normal hours', but be more generous as workers would continue to receive at least 80% of their pay for the time they are not working, or 100% if they are on the national minimum wage.
The JRS, which was announced at the onset of the UK-wide Coronavirus lockdown back in March, originally allowed employers to claim 80% of an employee's wages up to £2,500 from the Government.
However, as the economy began to unlock over the summer, the levels of support have slowly been withdrawn by the Treasury.
In August employers were required to begin paying employer National Insurance Contributions and pension contributions for furloughed hours themselves; and from this month they have also had to pay 10% contribution to every furloughed worker's wage.
During October that will rise to 20%, with the scheme closing permanently at the end of the month.
Last week, Labour leader Sir Keir Starmer called for a new sector-specific furlough for the parts of the economy most affected by ongoing restrictions, but this has reportedly been rejected by Sunak, who believes the furlough scheme is keeping people in 'suspended animation'.
About three million people are still supported by the JRS, which has cost £39.3bn up to September 20.
The FT estimates that if three million people joined a CBI-style work subsidy scheme it could cost the Treasury about £500m each month.