The move to reduce their hours from 37 to 36 will save £1.5 million a year.
Details of the plan were put to the full council when it met to consider its 2016-17 budget options ahead of the Scottish Government’s local government funding settlement.
Negotiations with the unions started in February to try and agree new terms and conditions which will deliver the saving without the need for compulsory redundancies.
The unions are looking for a number of assurances from the council in return for an agreement on the changes.
Subject to the successful conclusion of these discussions, the unions intend to consult then ballot their members on the proposals.
The timescale has still to be confirmed, but a successful ballot will see the deal back before councillors for final consideration ahead of its budget meeting on February 17.
Council leader Craig Martin said: “We have worked closely with the trade unions to produce a package of measures that will save the council over £1.5 million in staffing costs.
“In return we have agreed that subject to there being no significant further adverse changes to the revenue budget over the period of the current budget strategy, the council council responds to the agreements that the unions wish to seek by having no compulsory redundancies, reinstating these savings if budgets improve and seeking no other staff savings before the next council elections in 2017.”