The US National Hurricane Center (US NHC) says interests in the Leeward Islands should monitor the progress of Tropical Storm Lee.
The system is located about 1,315 miles (2,115 km) East of the Lesser Antilles.
The NHC says Tropical Storm Lee is expected to rapidly intensify into an extremely dangerous hurricane by the weekend.
No watches or warnings have been issued.
At 5 PM AST (2100 UTC), the centre of Tropical Storm Lee was located near latitude 13.2 north, longitude 41.8 west.
Lee is moving toward the west-northwest near 16 mph (26 km/h), and this motion is expected to continue for the next few days with a slight reduction in forward speed.
Maximum sustained winds have increased to near 45 mph (75 km/h) with higher gusts.
Lee is forecast to be a hurricane within a couple of days and will likely become a major hurricane by Friday.
Tropical-storm-force winds extend outward up to 70 miles (110 km) from the centre.
