Forecaster James Franklin of the National Hurricane Center in Miami said the depression could become a tropical storm by Wednesday, and at that point it would be named Isidore.
"Most of the strongest winds with the depression are located well to the north and east of the center," Franklin said. "Gusts to tropical-storm force may spread over Jamaica over the next day or so."
He said the rains could cause life-threatening flash floods and mudslides.
No official warnings were issued for Jamaica, but they were under consideration.
Tropical depression No. 10 formed for the first time Sunday, but deteriorated before developing again two days later.
At 11 a.m. EDT, the center of the system was located near latitude 15.9 north, longitude 77.2 west or about 145 miles south of Kingston, Jamaica.
The depression is moving west near 9 mph, and a turn to the west-northwest is expected. The official forecast shows the system approaching hurricane strength off the western tip of Cuba by Friday, but there is still the possibility of a move toward the north and south Florida.
The depression had deteriorated into a tropical wave with no closed circulation Sunday, but hurricane hunter aircraft were sent into the system Tuesday and found the circulation had closed up again.
Because the circulation center is new, forecasters said early forecasting will be more difficult than usual.