If you are thinking about just the basic FHA mortgage, the answer is "no."
Under current guidelines, FHA lenders will approve a maximum base mortgage loan equal to 96.5% of the purchase price. They will use 96.5% of the "appraisal value" if that value is lower than the purchase price.
This makes sense for 2 reasons: (1) the lender does not want to be on the hook (right out of the starting gate) for a loan that is more than the property is worth; and (2) "YOU" do not want to pay $275,000 for a property worth $225,000. Then YOU would be in a losing position (upside down) right out of the gate.
The pre-approval amount is not related at all to the actual purchase price or appraised value of the actual home you end up selecting. The pre-approval was merely a guide so you and your realtor would know where to focus your search efforts. No need to look at penthouses if your approval is for a townhouse. :-)
Hope things went well.
Carol Lloyd, CLU, ChFC, FLMI
"In the Business of Educating My Clients About Mortgages"
First Hallmark Mortgage