Flossie was located 280 kilometers (170 miles) from the port of Manzanillo in the Mexican state of Colima, the meteorological agency said in its latest report.
It was generating maximum sustained winds of 120 km/h (75 mph) and was moving at 17 km/h (10 mph), it added.
The storm is expected to move parallel to the Pacific coast until it moves away from Mexican territory, likely leading to rain in the states of Michoacan, Guerrero, Colima, and some areas of Jalisco and Oaxaca.
"The rainfall could cause landslides, rising river and stream levels, Mexico's National Water Commission said in a statement, adding that flooding in low-lying areas could also be expected.
Although a direct hit from Flossie is not expected, President Claudia Sheinbaum urged residents to "exercise extreme caution" in a message posted on social media on Sunday.
Mexico is hit by cyclones every year, both on the Pacific and Atlantic coasts, usually between May and November.
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