Northern Ireland's Health and Social Care board has said it is in discussions with the Northern Health Trust about the feasibility of extending the opening hours of the Mid-Ulster Hospital minor injuries unit.
Health Minister Michael McGimpsey has asked the trust to look into the possibility of extending the opening hours for the unit.
The hospital's accident and emergency department was closed earlier this month.
It was downgraded to a minor injury unit due to safety concerns.
In a statement released to the BBC, the board - which organises and pays for the delivery of health services - said it was now involved in discussions regarding the feasibility of keeping the unit open longer during the week and at weekends.
The board stressed that it was not a financial issue, it was whether or not it could provide a safe environment for both patients and staff.
Earlier, Vice Chair of the Health Committee Sinn Fein MLA Michelle O'Neill said she would support longer opening hours.
"If they were available at weekends and evenings, I think that's something that the community would very much welcome," she said.
"It's something that I want to pursue further with the trust and with the staff who work on the hospital site."
On Friday, the SDLP's Patsy McGlone said that "mooted calls for extended opening times" at the unit "is not enough to properly serve the health needs of the local people".
He said that they "can only be properly served with the re-introduction of accident and emergency services to the Mid Ulster Hospital".