The authority is to cut at least 2000 jobs over the next four years in a bid to save £141 million.
Compulsory redundancies are not being ruled out and some council services – such as buildings management – may be privatised in the savings drive.
Bosses at Unison’s Edinburgh branch fear total job losses could run to more than 3000, although this has been dismissed by senior council sources.
They have warned that council staff could take strike action if there are compulsory redundancies.
Unison branch president John Stevenson said there was a possibility of strikes.
“There is now the possibility of compulsory redundancies,” he said. “We have a standard policy of balloting our members on taking industrial action should that possibility arise.”
Branch secretary Amanda Kerr said: “The effect of cuts on services and staff will be devastating as at least 15 per cent of council employees could face being forced out of their jobs. Losing this amount of staff will decimate the services we provide and the public rely on to the point where they would be unrecognisable.”
City bosses stressed that an “improved strategy” for purchasing goods and services had already delivered savings worth £39m, with a further £6m to be secured each year thanks to a new IT contract.
Councillor Alasdair Rankin, finance leader, said: “Realistically, to make the necessary savings, we have little option but to consider reducing the number of people who work for the council.
“Bearing in mind we are keenly aware that this is about people, we will work closely with our staff and the trade unions during this difficult time.”