The Fiji Meteorological Service says a tropical depression to the west of the Samoas could develop into a cyclone within the next six to 12 hours.
However, the US National Weather Service has downgraded the Tropical Storm Watch for the territory to a high wind warning as the system moves away.
American Samoa meteorologist Elinor Lutu McMoore said because of its size people will continue to experience heavy rain and winds over 60kmh throughout the day.
"The main concern for us right now is the trough that is associated with the depression that is the one that is right over American Samoa right now and it is bringing us and it will continue to bring us a lot of rain.
"So that is our main concern the flooding. And then it is still going to bring us winds."
Most schools are closed today because of the weather.