Unions want a “flat cash pay offer” where everybody would receive the same amount of money.
Talks to try to end the council strike in Scotland are entering a fourth day.
Bin strikes now affect two thirds of Scotland’s local authorities and rubbish is building up in many town and city centres.
Unions are reiterating their claim for a “flat cash pay offer” where everybody would receive the same amount of money.
They are seeking an agreement similar to the one made to council workers in England, which included a £1,925 flat rate pay offer.
The unions say that offering a percentage pay rise would mean the most money would go to the best paid staff.
Local government umbrella organisation Cosla held a meeting with council leaders on Saturday to discuss a potential proposition.
Unite regional officer Wendy Dunsmore told BBC Scotland they are anticipating an offer in the “very near future”.
It came after Public Health Scotland warned of a human health risk from overflowing waste, and advised councils to decontaminate areas where bins have overflowed.
The bin strike began in Edinburgh on 18 August, in the midst of festival season, after the unions rejected an initial pay offer equivalent to a 3.5% increase.
It escalated last week when refuse workers at a further 20 local authorities, including Glasgow, Aberdeen and Dundee, walked out despite a revised 5% offer.
Cosla had described it as “one of, if not the best offer in decades for Scottish local government workers” with some workers getting an overall 7.36% increase.
The Scottish government has given an additional £140m to councils to help fund a pay increase for staff.
But the unions – Unite, Unison and GMB – are calling for more funding from the government to pay for an improved offer.
And they have refused a government request to suspend strikes while negotiations are held with Cosla.
Talks between Cosla and the unions are expected to resume at 14:00 on Sunday.
The council unions sense they are in a very strong negotiating position.
The strike is having a major effect on refuse collections in much of Scotland and leaving town and city centres filthy.
The threat of a second strike in just over a week means these scenes could be repeated.
This is something nobody wants to see happen.
The unions want a “flat cash offer” rather than a percentage pay rise. This means everybody would get the same pay rise but the most benefit would go to the lowest paid.
A straightforward percentage rise would mean that senior staff would get the most.