Tropical Cyclone Osai is the second cyclone in a week passing the Cook Islands, while there is an orange alert for parts of French Polynesia due to cyclone Nat.
The director of Emergency Management Cook Islands John Strickland said Osai will likely to go west of Palmerston instead of following the same direction as cyclone Nat.
Warnings for gale winds, and strong winds have been issued for parts of the southern islands by Fiji's metservice.
A coastal inundation warning is in place for low lying coastal areas of Palmerston.
Strickland said Palmerston has been experiencing north-easterly winds of about 46 kilometres an hour, and rain.
He said the island is prepared.
The Fiji Meteorological Service said as of 5am Wednesday, Cook Islands time, the storm was about 250 kilometres west-northwest of Palmerston Island and moving south-southeast at about 15 knots (approximately 28 kilometres per hour).
Cyclone forecaster Sakeasi Waibuta said the storm is taking a similar path to Nat but is moving more south.
"A special weather bulletin has been sent for the Southern Cooks especially for Palmerston Island, due to expected gale force winds, 34 knots to 47 knots," he said.
"Currently it's a category 1; it's expected to intensify to a category 2 as it moves closer to Palmerston Island."
Waibuta said the cyclones impacts will start being felt later today on Palmerston.
French Polynesia on alert
Meanwhile, some schools in French Polynesia will be closed on Wednesday local time (Thursday NZ time) due to tropical cyclone Nat, which is back to a category 1 storm.
The main hospital in the capital Papeete will also run on a reduced mode.
French authorities have place an "Orange" level (described as "pre-alert") over parts of the territory.