Dalila, with maximum sustained winds of 65 mph, was about 165 miles west-southwest of Manzanillo, Mexico, moving west-northwest at 7 mph, the National Hurricane Center in Miami said in its 2 p.m. PDT advisory.
Earlier tropical storm watches and warnings were discontinued by the Mexican government.
Dalila was expected to turn west with a decrease in forward speed over the next couple of days and could become a hurricane by Tuesday.
Tropical-storm-force winds extended up to 70 miles from the center.
Dalila was expected to produce between 1 and 3 inches of rain over coastal portions of the Mexican states of Michoacan, Colima and Jalisco, with localized totals of 5 inches.