The NHC says the storm could become a major hurricane. The minimum central pressure estimated from Air Force Hurricane Hunter observations is 980 millibars.
The system now poses no threat to land and no watches or warnings are in effect. A slightly faster west to west-northwest motion is expected during the next two days.
Meanwhile, Katia went from being a tropical depression to a tropical storm to a hurricane in the space of a few hours off the coast of Mexico. Forecasters predict that by Friday, it will have turned into a Category 3 hurricane.
It is feared the storm may strengthen to a potentially devastating category three hurricane, which can bring winds of up to 129mph.
Stay with WAVY.com for the latest updates.
The closest land mass Jose will approach is the northern Leeward Islands, the same ones Irma just devastated.More news: A Massive Black Hole in the Center of the Milky Way
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Tropical Storm Katia is over the southwestern Gulf of Mexico about 135 miles east-southeast of Tampico, Mexico, the hurricane center said.
Hurricane Jose is in the open Atlantic, some 815 miles (1,310 km) east of the Caribbean's Lesser Antilles islands. Such a watch means that hurricane conditions are possible, in about 48 hours.
The storm is forecast to produce up to 10 inches of rain, with the possibility of 15 inches in northern Veracruz, according to the National Hurricane Center.
The NHC this morning advised that interests in the Leeward Islands should monitor the future progress of Jose, which could become a hurricane by Friday.
Right now, Jose is following about two days behind Irma, forecasts show.
Jose is now out at sea but is heading west at a speed of around 13 miles per hour.
No watches or warnings are in effect for Jose. In Barbuda, an island east of Puerto Rico, winds ripped off the roof of a police station, forcing officers to take shelter in a nearby fire station, The Associated Press reported on Wednesday.