Forecasters at the National Hurricane Center in Miami said Sunday that Danielle had maximum sustained winds of 40 mph (65 kph) and the storm is expected to strengthen over the next couple of days.
Meanwhile, Tropical Storm Frank developed in the Pacific off Mexico, and storm warnings have been issued for parts of the coast.
Forecasters said the storm had maximum sustained winds of 60 mph (95 kph). It was about 130 miles (205 km) south-southeast of Puerto Angel, Mexico. It was moving west at 8 mph (13 kph).
Mexico has issued a tropical storm warning for the coast from Puerto Angel west to Acapulco. Frank is forecast to move parallel to the coast through Tuesday.