The chief executive of a Devon NHS Trust has said savings of £27.5m will mean "tough decisions".
Plymouth Hospitals NHS Trust, which manages Derriford Hospital and employs about 5,500 people, must decide how to make the cutbacks.
Chief executive of the trust, Paul Roberts, said savings could be made by reducing the use of agency staff as well as over-time costs.
But unions have warned that any cuts would affect services.
Mr Roberts said: "We've got to make tough decisions that are the best decisions for staff and most critically for patients too.
"If we can reduce things like agency costs and over-time costs which are quite expensive, that means we have to reduce fewer posts.
"There's a lot that we can do to improve the efficiency, that includes back-office services like personnel management."
The hospital currently has an annual budget of more than £370m, but all the trust's departments have been told that they will face budget restrictions to make the savings.
Hospital bosses have also been told that patient care must not be affected.
Mr Roberts said: "We also have to make our clinical care more efficient, if we can do things more efficiently patients will have to stay in hospital for less lengths of time.
"There are many things we have to focus on to make sure that making savings doesn't affect the care we provide to patients."
However, unions have said that any cuts are bound to have an effect.
Stuart Fegan, from the GMB union, said: "I think people are going to have to accept that if these cuts go ahead that the levels of service and professionalism that our members and others have provided is simply not going to be there.
"People have to ask the question whether they are willing accept that level of service reduction."