The website for the Tampa International Airport states that the following companies are located on airport: (car rental company links open in new windows)
The car rental counters are located across the walkway in the RED Baggage Claim Area and across the walkway in the BLUE Baggage Claim Area.
The rental cars for each of these companies are located in the parking gargage, directly adjacent to the car rental counters; no shuttle bus is required to get a rental car from one of these companies.
There are off- airport companies as well... courtesy vehicle service to those companies is available at either end of the Red and Blue Baggage Claim.
Thanks for your question, and hope this helps!