Company Americold is still waiting for more Covid-19 test results, with four staff already having tested positive.
The company's closed two sites - one at Mt Wellington, where the first positive case - a man in his 50s - worked, and the airport precinct.
Americold managing director Richard Winnall says all four cases were at their Mt Wellington facility.
"We're still awaiting at that site approximately half of the employee's test results back, and we hope to get those test results back today."
Winnall says they're waiting for just one final test result at the airport site - and if it's clear should be resuming operations.
He says there's no link between the outbreak at one of their facilities in Melbourne and the cases here.
Winnall told Heather du Plessis-Allan the facility in Melbourne is a totally different supply chain with product flow going in different directions and from different sources.
"I see no relationship at all, and I've made a lot of inquiries to satisfy myself on that."