The National Hurricane Center said the storm, located east of the Lesser Antilles, was packing winds of 120 miles per hour (195 kilometers per hour), as it moved northwest at nearly 18 miles per hour (30 kilometers per hour).
"Some additional strengthening is possible during the next 24 to 36 hours," the NHC said.
Hurricane Irma - at Category Five, the highest level on the Saffir-Simpson scale - battered a string of Caribbean islands on Wednesday and appears to be on a collision course with southern Florida.
Besides hurricanes Jose and Irma there is another Atlantic hurricane, Katia - a Category One storm - in the southwestern Gulf of Mexico.
According to meteorologists the last time there were three active hurricanes in the Atlantic at the same time was September 2010.
More to come
