A Treasury delegation conducting negotiations in Iceland has released a statement saying that "significant progress" has been made.
A deal has reportedly already been done in principle over an "accelerated" payment for small UK depositors, although the situation with larger investors has yet to be resolved.
Most of the estimated £1 billion invested in Iceland by councils was capital, but according to reports, some had deposited revenue budgets - which include payroll - in order to earn interest.
A spokeswoman for the Local Government Association (LGA) stressed that all councils held reserves, and it is "highly unlikely" there will be any impact. "We are not aware of any councils that have immediate cashflow problems in terms of services or paying staff," she said.
The LGA is urging the Government to relax capitalisation rules for hard-hit councils and allow them to delay payments of business-tax rates if necessary.
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