Peters said the travel bubble depended on both countries having tight borders.
"The protocols could be put in place in two days flat, quite frankly, but what you need to have ensured is the maritime and aviation surveillance in both countries is good enough to assure us that we've got a safe bubble."
Peters said a team in the Ministry of Foreign Affairs was still working on the arrangements and he continued to think it was a "great idea".
He also said the travel bubble "New Zealand's idea - not Scott Morrison's".
Morrison said on Friday his priority was to reopen Australia's state borders but was still keen on organising travel arrangements with other countries.
"I'm trying to get the New Zealand travel bubble back in place, and I'm sure we'll take that up again soon," he said.
"I'd like to see that also if we can among the Pacific nations ... Japan is keen to do it, Singapore is keen to do this and there are a number of nations that are happy to do this with us. I can see that as the next step, but right now we're trying to get domestic borders open."
Last month, before the resurgence of Covid-19, Prime Minister Jacinda Ardern said she hoped a travel bubble with the Cooks Islands would be up and running before the end of this year.
A draft agreement has been drawn up and phase two will be for director general of health Ashley Bloomfield and his Cook Islands counterpart to sign it off and to stress-test the system.
Bloomfield said today the Health Ministry was one of the agencies involved in the planning, but that work had been put on hold while it managed the outbreak.