As of 2 p.m. ET, the system is about 415 miles east-southeast of Port O'Connor, Texas, with maximum sustained winds of 35 mph as it moves to the west-northwest at 11 mph.
Slow strengthening is expected and the system is forecast to become a weak tropical storm, named Hanna, in the next day or so.
Tropical Storm Hanna is forecast to make landfall Saturday along the coast in South Texas. Tropical storm watches are in effect along the Texas coast from Port Mansfield to High Island, with conditions expected by Friday night.
The current forecast shows the system will be very weak at landfall.
According to the NHC, isolated amounts of up to 8 inches of rain are possible, along with life-threatening surf and rip currents along much of the Texas and Louisiana coasts.
Gonzalo poised to be the first Atlantic hurricane of 2020 season
Tropical Storm Gonzalo set a record for the earliest named seventh tropical storm, "G" storm, of the Atlantic hurricane season.
As of Thursday afternoon, the system had weakened a bit, with maximum sustained winds of 60 mph and is about 850 miles east of the Southern Windward Islands, moving west at 14 mph.
The small and compact Gonzalo is moving westward and is forecast to strengthen into a hurricane over the next few days. A hurricane watch is in effect for Barbados as well as St. Vincent and the Grenadines.
Tropical storm-force winds extend only about 35 miles outward from the center of the storm, according to the NHC.
Gonzalo will approach the Windward Islands late Friday and Saturday, possibly as a hurricane, but once it gets into the Caribbean, environmental conditions become pretty harsh, and the storm is forecast to weaken significantly.
It remains too early to gauge whether Gonzalo will survive through early next week.
The 2020 Atlantic Hurricane Season will include the names: Arthur, Bertha, Cristobal, Dolly, Edouard, Fay, Gonzalo, Hanna, Isaias, Josephine, Kyle, Laura, Marco, Nana, Omar, Paulette, Rene, Sally, Teddy, Vicky and Wilfred.