However, this evening his office clarified that means testing and asset testing was not being considered.
Support services for older people are funded by district health boards (DHBs), and are designed to help people stay in their home for as long as possible.
They may include help with personal care such as showering and dressing, and cleaning and meal preparation.
People who want to receive support services must currently have a needs assessment carried out.
Ms King said the home care sector was facing a financial crisis, with providers struggling to keep up with minimum wage increases.
That was outlined in a report presented to the Government before last month's Budget, Ms King said.
"Many organisations that look after our elderly in their own homes say they are operating at, or very close to, loss."
Julie Haggie, chief executive of the Home and Community Health Association, said she understood the wider funding picture for elderly support would be reviewed this year.
The Government was trying to work out how to cope with increasing costs, Ms Haggie said. Any changes would need to be carefully weighed.
"You need to look at how people react if they have to pay for care in their own home, and whether that will encourage them to be more mindful of their care, or whether it won't.
"You do need to make changes sometimes in health. We think though that currently it is really efficient and cost effective to help people remain at home. And you don't want to lose that."