Tropical Storm Dorian developed Saturday afternoon in the central Atlantic, east of the islands.
A general west-northwest track will take it into the Caribbean by Tuesday.
Dorian will likely become a hurricane this week, once in the Caribbean.
The islands in the Caribbean are at risk from the storm.
However, local weather expert, WWL-TV meteorologist Chris Franklin says Dorian should not pose a threat to the Gulf of Mexico.
"Models indicate the storm will dissipate as it approaches Puerto Rico and the Dominican Republic," says Franklin.
A tropical storm warning has been issued for Barbados as the fourth tropical storm of this year's Atlantic hurricane season moves toward the Lesser Antilles. The U.S. National Hurricane Center in Miami says Tropical Storm Dorian could intensify to near hurricane strength over the eastern Caribbean Sea by Tuesday. As of 11 a.m. EDT Sunday, the storm's center was located around 465 miles east-southeast of Barbados and was moving west at 14 mph. Maximum sustained winds remained near 40 mph. A tropical storm watch was issued for St. Lucia and St. Vincent and the Grenadines. Watches for additional islands in the Lesser Antilles will likely be issued later Sunday. The advisory says Puerto Rico, the Dominican Republic, and Haiti should monitor the storm's progress.