Tropical Storm Barry, which is currently moving over the Gulf of Mexico, is likely to develop into a hurricane.
It is forecast to hit the US city of New Orleans, which has already seen thunderstorms and flash floods.
A state of emergency is in effect and residents in some low-lying areas have been asked to evacuate.
The Mississippi river could come dangerously close to overtopping banks shielding the city, officials warn.
It could rise as high as 20ft (6m) above sea level, they say, potentially exceeding the 20-25ft levees which protect the river from overflowing.
“We’re confident the levees themselves are in good shape. The big focus is height,” Ricky Boyett, a spokesman for the US Army Corps of Engineers, which maintains the fortifications, told AP news agency.