Nottinghamshire County Council is considering handing over some of its services to the private sector, including catering and highways.
The authority will ask private companies how they would run these services and what they would charge.
County spokesman Tim Malynn said the review was a starting point for saving £120m over the next four years.
Mike Scott of Unison said: "We are really quite horrified about this as it came as a bolt out of the blue."
The county spends £60m and employs 3,000 people in the services it is thinking of privatising.
"We realise that the council has got to cut back but this is not the way to do it," said Mr Scott.
He said the cuts were not inevitable and the union was willing to work with the council to find other ways to bring about savings.
"The council seems hell-bent on privatisation and that is what this is all about."
Mr Malynn said £1 in every £4 that the government needs to saved will come from local council cuts over the next four years.
He said: "Like every other council in the country, we are facing massive financial pressures and we must look seriously look at who is best placed to provide some services."
He added any county council employee who is working at a job that is transferred to another supplier would transfer with the job.
He said the council would remain responsible and accountable for all its services regardless of who provides them.
No decisions will be made until after a full review has been completed and a final decision is expected a year from now.