It could mean the council, Scotland's biggest, will look for 1000 redundancies, on top of the almost 3000 staff who have left since 2010.
Staff and political groups at the council will be briefed today on the need to save more than £48m between 2013 and 2015.
It is understood the council will stick to its policy of no compulsory redundancies, that not everyone who asks will be allowed to go and that certain departments will be targeted for lay-offs.
But unions have warned that further job losses will stretch an already threadbare staff to breaking point and impact on the authority's ability to deliver services.
Other avenues to make savings which are expected to be advanced include, cuts to social work and education budgets, which account for 70% of the council's spend, and joint ventures with the private sector on services like roads and lighting.
The news broke a week after North Lanarkshire Council announced it would have to save £74m over the next three years, with options for cuts including school and care home closures, cuts in workers' terms and conditions and staff lay offs.
Glasgow is only the second authority in Scotland to make known the spending pressures it faces in the next few years, with others expected to follow suit in the weeks ahead.
Glasgow's cuts are not as severe as those in North Lanarkshire, largely due to it making annual savings of around £45m in the past five years.
However, there are fears the reduction expected in public spending after 2015 will dwarf the current cuts.
A council source said: "We've been at the forefront of saving money for a good few years now, but what is there left to cut?
"You start getting into the realms of the previously unmentionable. Stuff like sick pay perhaps. Closing the pension fund to new entrants.
"What we'll probably have to look at is bringing together all the back office stuff, which is still done by each department, and look to see if the redundancies can be made here."
Another said: "This is a huge sum of money over two years, even if some of our decisions to protect ourselves, like the Aleo structures and early settlement of equal pay, has paid off.
"You can't oversell the challenges facing Glasgow and local government in general.
"We're not saying we can no longer do stuff but, neither can you give any assurances."
Brian Smith, of Unison, said: "What does targeted mean? That it's social workers or nursery workers? With another four-figure number of staff going out the door this will seriously affect frontline services."
The council cuts amount to more than £28m across 2013-2014 and £20m in 2014-2015, based on, among other factors, a reduction of £8m in how much the authority gets from the Scottish Government.
But the council has forecasted that by 2015 this could rise to a real terms reduction of £49m, or 6.3% of the council budget.
On top of that, a recent report by the Centre for Public Policy for the Regions claimed that if there was a continuation of the policy of protecting NHS budgets then council grants from Holyrood could fall by 9.9%, in Glasgow terms a cut of £70m-plus.
A council spokesman said: "This forecast sets out the financial challenge facing all local authorities in Scotland now and in the foreseeable future.
"We have taken some big, difficult decisions in the last few years and over the autumn we will be putting together a package which will continue to take the city forward."