York Hospitals NHS Foundation Trust says it needs to make £30m in savings over the next three years.
The trust, which runs York District Hospital, said the decision had been made in response to "financial pressures" facing the health service.
Chief Executive Patrick Crowley said: "We have asked all of our staff to tell us their ideas for how money can be saved."
He added staff car parking charges had been increased to raise income.
A trust spokeswoman said it hoped the need for job losses would be avoided and front-line services could be protected.