Ministers may make the furlough scheme more flexible - and less generous - under changes expected to be announced next week.
Clarification on the future of the £39bn scheme comes ahead of a May 15 deadline for consultations on large redundancies, which legally require 45 days. It is due to end on June 30.
Options under consideration include allowing furloughed staff to return to work for one or two days and reducing the amount each employee receives.
Sources said this could include moving to a co-payment model such as Germany's Kurzarbeit scheme, whereby the state and employers split payments above a certain level.
Sectors such as hospitality face far bigger challenges in restarting under continued social distancing, with some more reliant on seasonal income. "These will need some form of ongoing support," said the source.
The CBI has been in discussions with the Treasury over the shape of future support amid concerns that a sector-by-sector approach may be too complex.
The discussions come as relations between the business lobby group and government have thawed significantly, following tensions over Brexit.
According to sources in other business groups, the CBI has managed to build up a strong relationship with the Government as others have been sidelined.
Rain Newton-Smith, CBI chief economist, said government economic support must evolve.
“Support for sectors prevented from reopening by continued social distancing rules should continue in some form. The scheme will also need to encourage the transition back to employment as demand returns,” she said.
British Chambers of Commerce director-general Adam Marshall said: "A sector-based end to the furlough scheme would have serious unintended consequences across the country because you create arbitrary dividing lines between companies, many of whom operate in the same supply chains."
A Treasury spokesman said: “The Coronavirus Job Retention Scheme is an absolutely crucial element of our financial support in protecting jobs and businesses through this crisis and has already supported millions of workers across the UK. Future decisions around the scheme will take into account the wider context of any lockdown extension, as well as the public health response, so that people and businesses can get back to work when it is safe to do so.”