More than 200 posts could go at the Shrewsbury and Telford Hospitals NHS Trust, officials have said.
The trust, running hospitals in Telford and Shrewsbury, said it also wanted to cut the amount spent on agency staff.
It failed to reach a target of saving £12.1m last year, managing to make savings of £3.2m, and said it needs to save about £10m this financial year.
A spokesman said the trust was facing difficult times and would try to protect frontline staff.
Closing the 200 posts would save about half of the required £10m, BBC Midlands Today health correspondent Michele Paduano said.
The trust said the total planned income for this year was about £280m.
A spokesman for the GMB said hospital staff were concerned and demoralised.
Last month, proposals to reorganise some services at the two hospitals were approved by the NHS trust boards.
The plans include moving children's and maternity services from the Royal Shrewsbury Hospital to the Princess Royal Hospital in Telford.
Hospital officials have said the proposals are in patients' interests.
The Shrewsbury and Telford Hospitals NHS Trust is putting together an outline business case, possibly published by July.