Oh, my goodness, there are so many factors that go into How are REOs selling in your geographic area? In my area, only about 1% of the properties under contract are REOs, so there are not a lot of buyers for them. What is the condition of the property? The worse the condition, the less buyers want to pay. No one is going to do the work for free any longer. What is the actual market value of the property? Your offer should be based not on asking price but on market value. Are you buying a home for yourself or are you purchasing the property as an investment? If an investment, then determine a percentage off of market value less fix up costs and don't budge from that price.
The absolutely best advice I can give you is to find a realtor with actual and extensive experience working with REO buyers and do what they tell you to do.