Hernan was located 585 kilometers southwest of the tourist port of Manzanillo late Saturday and was moving in a northwesterly direction, parallel to the coastline, at a speed of 22 kilometers per hour, Mexico's National Meterological Service (SMN) reported at 0830 IST.
The storm was packing maximum winds of 65 kilometers per hour, with gusts up to 85 kilometers per hours, the SMN said.
The Miami-based National Hurricane Center, which had slightly different figures, warned that Hernan was picking up strength.
It added however that the storm is expected to weaken today.
Heavy rain from tropical storms Douglas and Elida earlier this month killed three people in the northern state of Chihuahua, while three other people were killed by Hurricane Amanda in May in the states of Michoacan and Guerrero.
Neither Mexican nor US weather monitors expect Hernan to make landfall.