The storm is forecast to soak parts of Cuba and Florida on its way north towards the US Gulf Coast, according to an NHC forecast.
At 1500 GMT Alberto packed winds of 40 miles per hour and was moving north-northeast at a speed of six miles per hour.
Alberto is expected to pass near the eastern coast of the Yucatan peninsula late Friday, reach the western tip of Cuba on Saturday, emerge over the Gulf of Mexico late Saturday, and on Monday approach the north-central US Gulf Coast — the states of Louisiana, Alabama and Mississippi, the NHC said.
It added that “gradual strengthening” is forecast for the next 72 hours.
Alberto is expected to drop between 10 and 15 inches (25 and 38 centimeters) of rain across parts of the Yucatan Peninsula and western Cuba.
“These rains could produce life-threatening flash floods and mudslides,” the NHC warned.
The 2018 Atlantic hurricane season, which begins officially on June 1, could bring 10 to 16 named storms, including tropical storms and hurricanes, the National Oceanic and Atmospheric Administration (NOAA) said on Thursday.
Last year was particularly devastating, with Hurricanes Harvey, Irma and Maria wreaking deadly havoc throughout the Caribbean and Atlantic basin.
They were among 17 storms large enough to merit their own names which tore through the Atlantic basin, including 10 hurricanes.
Tallied together, 16 major weather disasters in the United States, including hurricanes, cost the US $306.2 billion in 2017, breaking the previous cost record of $214.8 billion in 2005, said NOAA. (AFP)