Councillors met last Tuesday to discuss the issue, but the public were excluded from the meeting.
A council spokesman said it was not a final decision on the facility’s future, but the entry of the negotiation phase with Health New Zealand Te Whatu Ora.
If those negotiations were successful then a proposal would be presented to councillors to vote on.
Mayor Gary Kircher said "we want to reassure the community that these negotiations start from the critical position of maintaining a hospital and health services in Ōamaru, for the Waitaki district".’
The council took control of the hospital in 1999, and without it and Waitaki District Health Services Limited (WDHSL), the facility would have closed down in the 1990s.
"Ensuring the hospital service remains here is our priority, and initial discussions with Health NZ have been encouraging in that respect."
Chief executive Alex Parmley said the priority was to secure the long-term future of the hospital and to ensure staff were looked after during any potential transition.
"There is a lot to discuss."
Last year the hospital’s emergency department was closed three times due to staff shortages.
Last week WDHSL joint interim chief executive Hugh Kettlewell said returning operations of the hospital to HNZ would "absolutely" help stop those situations from happening again.