In addition to Mayport, Key West Naval Air Station and the NASA Flight Facility in Wallops Island, Va., are being considered.
US Sen. Bill Nelson wrote Navy Secretary Ray Mabus, arguing in favor of the Florida bases.
The Navy intends to have five bases around the world for the drones.
The US Government Accountability Office projected the drones would go into production in May.
The Virginian-Pilot said that the environmental assessments for the three proposed bases could be ready for public comment by late June.
The MQ-4C Triton drones can fly more than 24 hours at a time and survey 2.7 million square miles in a single mission. They can be used for surveillance and search-and-rescue missions, Nelson's office said.
The eight drones in the squadron would also bring 400 sailors and their families, a potential economic boon to whichever base is selected.
"Florida is also uniquely positioned to be able to respond to the US Southern Command area of operations," Nelson wrote. "... I hope that the additional benefits Florida would bring to MQ-4C Triton operations will factor in your decision."
Florida's bases, he wrote, are also equipped to host the drones because of how close they are to the Atlantic Ocean and the Caribbean Sea.