She said it is likely heavy rain will hit Bay of Plenty and Coromandel.
However, she cautioned about the uncertainty of predicting cyclone weather patterns, particularly more than a few days out.
WeatherWatch.co.nz said Cook is a "very intense but small-sized storm".
The weather forecaster also had concerns with a larger-sized low in the Tasman Sea joining forces with Cook to drag more flooding tropical rains to the North Island.
"This set-up could see rain returning to flooded parts of Bay of Plenty, for example, this Wednesday then intensifying as ex-cyclone Cook passes by over Thursday and Friday with torrential rain around eastern parts of the North Island; rain heavy enough to cause even further slips and flooding as possibly more than a months worth of rain yet again falls in just a couple of days," it said.
"As for the four day Easter weekend, it doesn't look stormy so much as it looks unsettled for many regions."
Flynn was not overly concerned with the low joining forces with Cook, expecting the low to remain just west of the South Island.
