Tropical Cyclone Oli is moving in a south-easterly direction over the Cook Islands but has slowed down on Tuesday.
After moving away from the northern Cook Islands, the cyclone's wind strength has dropped to about 14 knots, Radio New Zealand International reports.
The Fiji Meteorological service says the southern Cook Islands could experience damaging gale force winds in the next day.
People have not been told to stay indoors, but are being advised to take precautions and secure their homes in the event of strong winds.
Evacuation centres have been activated. There have been no reports of damage or injuries to date.