However, forecasters said, the GFS sends some increased deep tropical moisture from the system toward the Gulf Coast later next week.
The warning is in effect from Cameron, Louisiana, to Intracoastal City.
Tropical Storm Bret formed in the Atlantic Monday afternoon and is expected to impact the Caribbean as early as Tuesday. A Tropical Storm Watch means that tropical storm conditions are possible within the watch area, generally within 48 hours. Some slight strengthening is expected before the system reaches land, the NHC says.
"That storm is expected to strengthen and make landfall midweek and then move north inland", said Severe Weather Team 2's Brad Nitz.
The Atlantic hurricane season runs through November 30. The storm is located about 135 miles southeast of Trinidad in the Atlantic Ocean. Aruba and Bonaire are also under tropical storm warnings.
The chances of it becoming a tropical depression or storm in the next five days were raised to 40 percent.
National Hurricane Center forecasters are keeping an eye on two systems roiling in the central Atlantic and Gulf of Mexico that have the potential to become tropical cyclones.
Meanwhile, Tropical Storm Bret is moving along South America's northern coast. It appears to have weakened, with limited storms appearing on satellite, and its chances of development are 50 percent over the next five days.