Mr McCully said a significant number of New Zealand doctors and nurses had already expressed a wish to go. The Government would also put in extra funding.
The facility is being built by the British Government but will be run by Australia, which has contracted health company Aspen Medical for the role. It is expected to open at the end of the month and will have about 240 staff, many local.
He said Australia's Foreign Minister, Julie Bishop, rang him to offer New Zealand a role. "She confirmed there was space for New Zealand to become a significant partner in that initiative and they would welcome us."
Officials were putting together a detailed proposal to go before the Cabinet, but he expected "the Anzac endeavour" would get the go-ahead.
Australia's Prime Minister Tony Abbott announced Australia's role on Tuesday after getting assurances from Britain that any Australian medical staff who contracted the disease would be properly cared for. That included medical evacuations for those in the early stages of the disease to Europe or the UK while those at advanced stages would be treated in Sierra Leone.
Mr McCully said the same assurances applied to New Zealand health workers.
"We've put a very high premium on welfare, safety and evacuation issues."
The Government would also reassess the existing protocols for health workers returning to New Zealand.
A handful of New Zealand medical workers have already worked in Ebola zones.
The Ministry of Health has developed a protocol for returning medical workers - twice daily monitoring for 21 days. If symptoms show they are put in quarantine although there have been no such cases.
The Government has stopped short of stronger border restrictions because of the small number of travellers arriving from affected areas.
It relies on passengers to declare they have been in Ebola zones and they are then questioned to assess the risk of exposure.
Australia has boosted its border controls, requiring passengers to fill out 21-day travel records and compulsory temperature checks for passengers of concern.