"Heavy rains and gusty winds could begin over the weekend and continue through early next week," the Miami-based Hurricane Center said in an advisory issued early Friday.
Meteorologists put the chance of the system strengthening into a tropical storm at 30 percent over the next two days 60 percent by Wednesday.
While the forecast for Florida remained in flux, the system is likely to have a significant impact in the Caribbean over the weekend.
"Heavy rains, with the potential to cause flash floods and mud slides, are likely over Hispaniola and eastern and central Cuba during the next couple of days," said the advisory.
It's been more than a decade since a hurricane has made landfall in Florida.
The National Hurricane Center predicted 2016 to be the strongest hurricane season since 2012, according to its updated Hurricane Season Outlook released in August.
Forecasters now expect a 70-percent chance of having up to 17 named storms, of which as many as 8 are expected to become hurricanes, including up to four major hurricanes.
The hurricane season runs from June to November, but the two-month period from mid-August to mid-October poses the greatest risk for storm activity.
Historically, nearly 96 percent of major -- category 3, 4 and 5 -- hurricane days take place during this time period, according to NOAA.