With sustained winds of 195km/h, it is feared that Raymond could hit the same area of Guerrero state that was devastated by Tropical Storm Manuel last month.
Coastal towns and cities from the beach resort in Acapulco to Lazaro Cardenas in Michoacan state have been put on alert as heavy rains are expected to lash the area for some 72 hours.
Residents have been warned to stay away from rivers and streams as flash floods are likely. Schools in the area have been ordered to remain closed and the authorities in Michoacan said all maritime activity and road travel should be avoided.
Mexico is still struggling to recover from two deadly storm which hit the country almost simultaneously last month
The storm, which is some 200km south-southeast of the town of Zihuatanejo, is currently drifting northward, according to the US National Hurricane Center.