Three sources close to the matter said the property firm has put forward a debt restructuring proposal.
But the sources said creditors were unlikely to accept Evergrande's new pitch.
They cited low recovery prospects and growing concerns about the future of the world's most indebted property developer.
Evergrande did not respond to a request for comment.
The firm has more than $300 billion in liabilities and is representative of a crisis in China's property sector.
Authorities have tried to support the industry as troubles at various developers have worried global markets.
Evergrande defaulted on its offshore debt two years ago.
This coming Monday (December 4), the Hong Kong High Court will rule on a liquidation petition.
This week, sources said Evergrande offered to swap some debt held by offshore creditors into equity in the company and two Hong Kong-listed units.
They said it also offered to repay the rest with non-tradeable "certificates" backed by offshore assets.
A collapse of Evergrande has been a major concern for global investors while the Chinese economy struggles.
Property sales have slowed in the country and hundreds of thousands of homes are unfinished.
If the Hong Kong court orders Evergrande's liquidation, appointed liquidators would take control and arrange to sell the company's assets to repay its debts.