The latest positive wastewater sample was taken on Monday.
Green told Morning Report testing was ongoing in different areas to help determine where the positive samples were coming from, but those results would not be available until possibly Saturday.
Testing, however, will not determine whether people in the region were historical cases or active.
"That's why we're really needing people to come forward and get tested," he said.
"We know that this can be a difficult process for some people and the repercussions of that, so we are really looking to reassure people that coming forward and getting tested is important to us and the whole community."
He said it was essential people understood how important it was to get proper care for their family if they had the virus and that those who tested positive would be supported well.
"We have a whole support package for people who test positive in our community and that's in place ready to go," Green said.
Health authorities were not getting significant testing numbers after starting with additional pop-up testings last week. Green said the last time was there a positive result in wastewater, people had rushed to testing centres.
"We haven't seen that rebound this time. [Maybe] that's because we're much further out of the winter period now and the general level of viruses circulating in the community is down, so that means less disease in community, so less people symptomatic and coming forward."
With holidaymakers and returning family members expected over the Christmas period, MIQ capacity in the region was for around 40 people to self-isolate, if required, with more capacity on the way.
"We have a complex of facilities on the site of the hospital, which is our main complex. We've got additional mobile support for people, that we can park into places and things like that, and we've got more spots coming on across the region," Green said.
He said that network could expand depending on need over the summer and vaccination rates in the region were surging, after lagging behind the rest of the country.
"We expect to be at 90 per cent first dose this week and then move on to having a fully vaccinated community after that. That's really the most important thing that the community can be doing to be prepared for this."
