Pontefract Hospital's maternity unit could remain open as an on-demand service.
But after talks with an independent group of health professionals, Wakefield Clinical Commissioning Group (CCG) now says it's looking for a compromise between keeping the unit open full time and closing it down.
No final decision has been made, but NHS bosses are seriously considering opening the centre as and when mums-to-be are ready to give birth.
This could be complemented by the creation of a "family hub" at Pontefract, to ensure the hospital remains busy.
Speaking at a health scrutiny committee on Thursday, the CCG's director of operations, Ruth Unwin said: "What is emerging as our preferred solution is to have what would be, in effect, an on demand service at Pontefract, coupled with continuity of care.
"You'd have a situation where midwives get to know a woman during her pregnancy and then you have a team of about five or six looking after all of your ante-natal care."
Mums-to-be continue to have freedom of choice over where they give birth, though those with high-risk or complicated pregnancies are generally sent to Pinderfields, where consultants are based in the midwifery unit.
A public consultation on the issue is likely to start in October.
Ms Unwin added: "If this is the option we see through, it feels as though this will offer a really good use of resources and a really good service for women.
"What we want to do to complement that is by putting more services for women and families in Pontefract so that it's more of a family hub.
"We think that would give us a really viable service."
Under the plans, midwives employed by the local NHS Hospitals Trust, which runs Pinderfields, Pontefract and Dewsbury hospitals, would move between sites to meet demand.
Last year, Pontefract's maternity unit was closed for around six weeks because of a staff shortage, with women diverted to Pinderfields as a result.
The chair of the scrutiny committee, Councillor Betty Rhodes, said the trust needed to be more specific on details regarding staffing, but welcomed the latest development.
She said: "It sounds like it's going to be good news for people.
"We want to promote it as a good bit of news for the future, but we need to be sure that all scenarios have been considered now, and not as an afterthought."
Local Democracy Reporting Service