An extra £80m has been found for a pay deal to end the threat of strikes in schools, BBC Scotland understands.
Council leaders are due to meet later to discuss the new offer, which would then be presented to unions.
Unison had set a Wednesday deadline for a new pay deal, but council body Cosla asked for an extension to seek extra funding from the Scottish government.
The three-day action by Unison, Unite and the GMB is scheduled for 26, 27 and 28 September in 26 council areas.
The funding package, now understood to be worth nearly £580m, follows talks between Cosla and deputy first minister Shona Robison.
The Scottish government previously said that councils would need to use existing budgets to fund a better deal.
Unison wants a new offer by 12:00 while Unite said it would give Cosla until 17:00.
GMB Scotland also said it wanted a new deal by Thursday.
The planned strike action would include janitors and school catering staff.
The dispute is over a pay offer for all council workers other than teachers – who are covered by a different pay deal.
A number of councils – including Glasgow – have already said schools will close if the action goes ahead.
The most recent pay offer, made last week, was rejected by the three unions.
It would give workers at least a £1,929 increase in annual salary by 1 January 2024.
Cosla said the deal would have seen the lowest-paid local government workers receiving a 21% pay increase in two years.
Unions said it was not an improvement on the previous offer and said more was needed to help staff deal with the cost of living.