The National Hurricane Center's five-day forecast at 11 p.m. Thursday showed the storm at hurricane strength and headed toward the Savannah region by Tuesday evening.
Beaufort County Emergency Management director William Winn said he was "just watching" what happens with the storm.
"We've got to see what happens over the mountains of Hispaniola, and we'll look at it again in the morning," Winn said Thursday.
The storm was predicted to lose some strength over the mountains, but could gain power again as it moves over open water, according to the National Weather Service.
Meteorologist Joe Calderone said Thursday that it was too early to tell what impact the storm might have on the Lowcountry, but that Jeanne is predicted to be five to 10 miles off the coast of Hilton Head Island on Tuesday.