As of 5 p.m. ET, the storm was located 190 kilometers (118 miles) north of Cozumel, Mexico, and about 1,220 kilometers (758 miles) east southeast of Corpus Christi, Texas, the center said.
It was moving to the west northwest near 19 kilometers per hour (12 mph). It was expected to continue traveling northwestward over the next 48 hours.
If it continues on that path, it should approach the coast of the northwestern Gulf of Mexico on Friday.
Earlier Wednesday oil companies with off-shore platforms in the Gulf of Mexico were taking precautions amid threatening storm forecasts for the area around Mexico's Yucatan Peninsula.
The Shell company has begun securing current well operations in the extreme southwestern Gulf of Mexico and evacuated some people Tuesday and Wednesday.
"Our total expected evacuated personnel is approximately 70 people," the company said. "These personnel are not essential to core producing and drilling operations and will not be able to perform their normal work functions during the passing storm conditions. Production is not expected to be affected at this time."
Chevron said it was monitoring the system.