The hurricane has maximum sustained winds Tuesday near 100 mph and could become a major hurricane by early Wednesday.
Danielle is located about 1,110 miles east of the Lesser Antilles and is moving west near 20 mph.
Meanwhile in the Pacific, Tropical Storm Frank is moving parallel along the coast of southern Mexico. Frank's maximum sustained winds are near 50 mph (85 kph). The storm is located about 130 miles south-southwest of Acapulco, Mexico.
A tropical storm watch is in effect for Mexico's coast from Acapulco to Punta San Telmo.