For home selling, the steps involved are: getting your house ready for sale, listing your house, finding a buyer, and then finally selling & closing your house. For purchasing your house, a buyer will have a financing option. Typically when a buyer comes to buy your house, the buyer will work with a mortgage company to get his/her loan. The buyer can also pay cash for purchasing. At time of closing, a closing agent will be involved who will help you with the process and during closing your FHA loan will be paid from money received from Buyer's lending institution. Any remaining equity will be paid back to you.
So coming back to your question, if I understand it correctly, you really don't need to pay off the balance in advance in order to sell your house. You can do it but there is no need to pay off loan in advance.
I hope it helps. Good luck!
I would ask you why you want to pay the balance first and then sell it? Can you not sell it for more than the amount of the loan? If the sale price is higher than the loan amount still owed, you could sell it and have the balance of the loan paid off at closing. You would then receive the remainder (sold price - loan payoff = remainder) This way you do not need to come out of pocket for the balance up front. You can also talk to a local real estate agent/broker. They should be able to get you a CMA (Comparative Market Analysis) that will give you a very good idea as the to value of your home so you can make a better decision. Good Luck.