"The storm is now tracking south eastwards and is speeding up - although generally the storm system is slowly weakening now that's it's tracking away from the equator and into less favourable conditions," said Weather Watch.
The Red Cross is urging Kiwis to be prepared as the storm approaches and check they've got the essentials ready in case they need to evacuate.
It isn't completely clear when Hola was likely to make landfall in New Zealand, according to Weather Watch. Most data indicated this was likely to happen on Monday. But other predictive models scheduled its arrival for a day earlier or a day later.
MetService's latest forecast also predicts that the storm will strike here on Monday.
Cyclone Hola was a "compact" storm, Weather Watch said, which meant it was hard to precisely track its centre.
If the storm moved slightly east most regions would avoid the worst of its wrath as most of the serious weather would stay out at sea, according to Weather Watch's latest update.
However, much of the upper North Island - including Auckland - would bear the brunt if it shifted slightly west.