Your offer should be based on two things:
1. The amount that comparable properties in the area have been selling for in the last 6 months.
2. The condition of the property and how much it's going to cost to remedy any issues.
You'll have to determine also if the condition of the property has already been factored into the list price. Buyers very often make the mistake of looking at the list price, and automatically deducting the cost of fixing any issues they see. If the "homework" has been done beforehand however, you will often see that Fannie Mae typically prices their properties competitively from the start - already factoring in condition issues.
Additionally, Fannie Mae markets select properties under a program called Homepath. To make an offer on one, you'll have to find an agent and have them submit an offer through their website. Every situation is different, but Fannie Mae generally highly trusts the valuation opinion of the listing agents they hire to market these properties. If you try to lowball them, they will likely either outright reject, or ignore your offer completely - especially in the first 30-60 days. If the properties don't sell, as the market time increases to 90-120 days, you will typically see strategic price drops.
More often than not however, these properties are priced very well off the bat, and typically you'll see them sell from anywhere from 92-100% or more of list price (especially if there are multiple offer rounds). Hire a local agent who has a good grasp of the market to advise you accordingly.
Hope that helps!
What the seller paid at foreclosure is often irrelevant because the remaining balance on the loan at time of foreclosure does not reflect the current market value and also attorney fees and other foreclosure expenses added to the foreclosure sale but do not add any value at all to the property. You should have an exclusive buyers agent doing the research of sales of similar properties in the same market area and providing price per square foot, tax values, seller concession amounts and other hard data so that you can make a wise will informed purchase decision. If you have a full time agent with a Masters degree in Planning with Finance and over two decades of experience, working for you, you will likely do better in negotiations. I'd be pleased to provide that service. If you appreciate this answer, please give it a thumbs up, or if this was the most helpful answer, please say thanks with a best answer click.
You may also want to read the following: http://nchomesbylarryt.com/2011/11/01/buying-foreclosures-ha
First thing you should do - if you haven't already - is hire a Realtor to represent you. The seller will pay the buyer's agent's commission so it won't cost you anything. Next, have your Realtor do a Comparative Market Analysis (CMA) on the property using comps that have SOLD within the last 3-6 months that are within a 1 mile radius of the property. This will give you current market value and that is what you should base your offer on - not on what was paid for the property. The bank is going to want current market value since they have most likely rehabbed the property.