The hurricane has maximum sustained winds Tuesday near 100 mph (160 kph) and could become a major hurricane by early Wednesday.
Danielle is located about 1,110 miles (1,790 kilometers) east of the Lesser Antilles and is moving west near 20 mph (32 kph).
Meanwhile in the Pacific, Tropical Storm Frank is moving parallel with the coast of southern Mexico. Frank's maximum sustained winds are near 50 mph (85 kph). The storm is located about 135 miles (220 kilometers) south-southwest of Acapulco, Mexico.
A tropical storm watch that had been in effect for Mexico's coast from Acapulco to Punta San Telmo has been discontinued.