At its strongest, Bud should be a 115-mph Category 3 storm, the National Hurricane Center said.
Its churning center was about 255 miles (410 KM) south of Manzanillo Mexico, the center said.
"Further weakening, possibly rapid at times, is expected during the next 48 hours, and Bud is forecast to weaken below hurricane intensity by Wednesday night", the center said.
The latest public forecast showed Bud moving in a northwestern direction at around 7 miles per hour.
Two major category 5 hurricanes, Irma and Maria, ploughed through the Gulf of Mexico, the Caribbean and the U.S. west coast during 2017's extremely active Atlantic storm season, leaving a trail of destruction in their wake.
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Forecasters are also watching a weather system in the Caribbean, which the hurricane center gives a 20% chance of developing into a tropical depression or storm within the next five days. Unsafe ocean swells and rip currents may commence Tuesday.
"Bud is now a category 3 hurricane on the Saffir-Simpson Hurricane Wind Scale".
Southwestern Mexico should expect several inches of rainfall from Bud, with the possibility of ten inches in certain areas.
"People in the zones of the states with forecast of rains, wind and waves, including maritime navigation, are recommended to take extreme precautions and to comply with the recommendations issued by the authorities", Mexico's meteorological service said in a statement.
The 2018 hurricane season is here and after last year's devastating storms like Hurricanes Harvey, Irma and Maria, officials are warning residents and tourists alike to be prepared if severe weather comes.