The Western Health and Social Care Trust has said it does not have the resources to meet the demand for home care packages for the elderly.
The Trust's chief executive, Elaine Way, said the only way to fund sufficient domiciliary care for older people would be to close another front line service.
There are currently almost 200 people on the waiting list.
The admission was made in a Trust presentation to Derry City Council.
More than £18m was allocated to caring for older people this year but the Trust has already overspent by almost half a million pounds.
The Director of Primary Care and Older People's Services with the Western Trust, Alan Corry-Finn, said the Trust was working closely with the Health and Social Care Board to secure additional funding.
"We do get a lot of money but it's not enough," he said.
"We spend about £5000 on each care package on average but our population is growing older and getting more dependent so more care is required."
Mr Corry-Finn said other ways of providing care were being looked at but more investment would be needed year-on-year.
"We are prioritising those most in need but regrettably that means people are having to wait on care," he said.
"That means some people may have to remain in hospital for longer but we are risk assessing on a daily basis and liaising with families as well to make sure people get the essentials they require.
The Chief Executive of Age NI, Anne O'Reilly, said there was a need for a "fundamental review" of how social care is managed.
"They seem to be running out of time and running out of options, and in the midst of that there doesn't seem to be an agreed back up plan," she said.
"We need to adjust the way our social care is delivered so that we don't have people waiting unduly for services."
In six years time, there will be almost 10,000 more people aged over 65 in the Western Trust area than there are currently.
The Trust's chief executive, Elaine Way, said she "would be keen" to work with councillors in Derry to come up with alternative ways of providing domiciliary care.