The Vanuatu Daily Post reported that last month the two countries concluded a second round of maritime boundary negotiations in Belgium.
The disputed islands lie south-south-east of Vanuatu and New Caledonia and have been the cause of recent tensions after a French naval mission landed in January and planted their flag.
Vanuatu claims sovereignty over Matthew and Hunter.
Dominion of the islands includes the surrounding ocean and seabed with its commensurate commercial prospects.
The next round of negotiations will take place in Sydney later this year or early 2020.