The NHC said Wednesday that Jose poses no immediately threat to land.
As Irma bears down on the U.S. mainland, two other tropical storms have been upgraded to hurricanes within minutes of each other. Unlike Harvey, which moved to the north and strengthened rapidly, Katia is expected to stick close to Mexico.
The NHC said "interests in the Leeward Islands should monitor the future progress of Jose".
The National Hurricane Center forecasts Katia to move in a southwesterly direction and make landfall late on Friday, Sept. 8.
Two other giant storms - Katia and Jose - have grown to hurricane levels, and now trail the calamitous Category 5 Hurricane Irma, which has battered the Caribbean and is headed toward the southern coast of Florida.
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Previous forecasts projected Jose to become a hurricane on Thursday. It is the 11th named storm of the 2017 Atlantic hurricane season. Hurricane Irma has been gaining strength in the Caribbean for over a week.
As Katia stewed in the Gulf of Mexico Wednesday, Hurricane Irma hit a multitude of Caribbean islands with winds of up to 185 miles per hour on its way toward the United States. "Where Jose is concerned, the islands of the Lesser Antilles will be impacted by rough swells, particularly along the north and east coasts", Baig said.
A hurricane watch is in effect for Antigua and Barbuda, and a tropical storm watch is in effect for Anguilla, Montserrat, St Kitts and Nevis and Saba and St. Eustatius, according to the hurricane center.
Hurricane Katia (far left) forms as Irma heads west as Jose develops in the bottom right.
It's following a track close to Irma, though its path is predicted to shift east of the current Category 5 storm that's packing 185 miles per hour sustained winds as it whips through the Caribbean.
Florida is now preparing for the possibility of Irma.