The depression's maximum sustained winds decreased to near 30 mph (45 kph) Wednesday. But the National Hurricane Center says some strengthening is possible before its center reaches land Thursday.
If the depression becomes a tropical storm, it would be named Danielle.
A tropical storm warning has been issued for much of the Gulf Coast from Destin, Fla., to Intracoastal City, La., including New Orleans.
The depression is located about 245 miles (390 kilometers) east-southeast of the mouth of the Mississippi River and is moving northwest.
Officials have halted drilling on a relief well intended to permanently plug the blown-out well in the Gulf.