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At a meeting last month, the council agreed to an overhaul of its pay and grading structure after eight years of negotiations.
The new system would see 63% of those affected gain financially while 11% will have their wages reduced.
The highest drop in wages is expected to be around £11,500.
The GMB and Unite had earlier said they secured an additional £110m into the funding package to resolve key issues affecting "the vast majority of our members".
The two unions sent out a message to staff earlier warning the fire and rehire policy might be introduced, and saying the extra money was now "hanging by a thread."
GMB and Unite both wanted the council to table the offer so members can make a decision.
Both unions stated that if the council pursues the fire and rehire policy then the two unions will "immediately enter into dispute to secure the improved package and halt fire and rehire".
Glasgow City Council has been embroiled in problems over pay for years.
The local authority previously paid out about £770m after it emerged female workers in roles such as catering or cleaning had for years been receiving up to £3 an hour less than those in male-dominated areas such as refuse collection.
The new job evaluation scheme was designed to draw a line under the row by bringing pay scales into line with equality law, but it also meant some staff would face wage cuts, depending on what pay banding the new scheme placed them in.
