The GMB union said it would ballot staff at Scotland’s largest local authority if it did not ‘immediately withdraw’ proposed cuts.
In a consultative ballot of 1,000 staff, more than 80 per cent voted with 95 per cent in favour of industrial action.
The vote comes amid an on-going dispute over pay and working conditions.
GMB officer Benny Rankin said: “There has never been such a level of support for strike action in living memory.
“After years of pay freezes and seeing their standard of living eroded, our members have had enough.
“We don’t care if the financial problems are down to John Swinney’s cuts or failings in Glasgow City Council, enough is enough.”
Cllr Frank McAveety, leader of Glasgow City Council, said: “I’m surprised to hear of these claims from the GMB. When the budget options are put to the council next week, I believe there will be no grounds for the threat of strikes.
“We have consulted with the unions every step of the way and have delivered our pledge of no compulsory redundancies. Staff will also have among the best terms and conditions in the country.”