Forecasters are advising those in the watch area to prepare for winds as high as almost 60 miles per hour and areas of locally heavy rain and flooding.
If it continues on that track, it will stay safely to the west of Florida.
A Tropical Storm Warning has been issued from Intracoastal City, La. eastward to the mouth of the Pearl River at the Lousiana-Mississippi border. A tropical storm watch is in effect from Cameron Parish and west to Texas' High Island community in Galveston County.
The tropical system is forecast to move through the Windward Islands and near the eastern coast of Venezuela Monday night and early Tuesday.
Persons with marine interests in St Lucia are strongly advised to exercise extreme caution.
Regardless of development, heavy rains are expected over portions of Central America, the Yucatan Peninsula, Jamaica, the Cayman Islands, and western Cuba during the next several days.
The system's maximum sustained winds early Tuesday are near 40 miles per hour.
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Rain chances of around 70 percent for Monday are forecast to remain in place Tuesday and Wednesday before conditions ease on Thursday.
Rough seas are expected to continue on Wednesday and Thursday, with wave heights reaching 5 to 7 feet. Right now, the National Hurricane Center gives it an 80 percent chance of developing into a tropical depression or storm over the next five days.
The disturbance is getting better organized on its trek toward the coast will likely be upgraded to Tropical Storm Cindy before it makes landfall.
"But it's remarkable to have two potential tropical cyclones at the same time during mid-June", the website added.
Most areas will get four to eight inches of rain through Friday, but some areas could see even high totals.
A tropical storm warning was issued for Trinidad, Tobago, Grenada and the coast of Venezuela earlier Monday.