What do you mean by a "closed" Fannie Mae home?
If you're not yet working with a Realtor, find a Realtor to help you with making your offer.
It's not possible to buy any property in Tampa Bay below market unless you are paying ALL CASH and taking a lot of risk and buying at the foreclosure or tax deed auctions from the Clerk's office. You will not get clear title on those, will not be able to inspect and may also have difficulty removing the current tenant or owner from the property.
Also if you can see past the "ugliness" of most HUD owned properties you may be able to get an FHA 203K renovation mortgage to turn a sow's ear into a silk purse! http://www.HUDHomeStore.com
Also only $100 down on FHA with HUD owned homes--you will have to pay ALL OF THE CLOSING COSTS so it's really a minimum of 2% down.
Good luck! It is a Seller's Market right now and with so many CASH investors from Wall St. your best bet is going after a property restricted to an owner-occupant, http://www.HomePath.com
or Freddie Mac, you can't rely on Freddie Mac's website to be up-to-date so have your agent do a search for listings with Freddie Mac in the description.
Hope this helps.
All the best,
Alma Rose Kee, PA
Sold On Tampa Team