The National Hurricane Center has upgraded the chance of development with the tropical wave near Cuba to 40% over the next few days. Keep in mind that means any type of system so a depression would fit into that category. That seems like the most likely option should anything actually develop.
Another wave farther out in the Atlantic has a higher chance and could be the next named storm before the end of the week.
The main impacts of the Gulf wave will be to bring high rain chances to the area by Thursday and Friday. Locally heavy rain will be possible.