Liua is over the Solomons' Makira Island and is forecast to develop into a category two on the scale of one to five.
Its winds are weak, but forecasters are concerned about its slow pace and heavy rains.
The official cyclone season runs from 1 November to the end of April.
Chris Brandolino of the New Zealand climate and weather office, NIWA, said Liua comes even before forecasters have put together their cyclone outlook for the region.