There are a few things to consider. How is it priced compared to comps? How long has it been on the market?

Normally when a REO has been on the market for over 90 days a bank considers it an "aged asset" and will take less for it. You can also improve your chances of the bank taking a lower offer by removing contingencies and closing quickly. Banks don't like FHA loans because they have to meet standards. Banks take cash offers over financed ones even if the financed offer is higher. Banks also take less for a home towards the end of a quarter so they can get it off their books and don't have to carry it into next quarter.

Ben

Another important point to consider is other offers on the property you are interested in. There is no way to gauge how much to offer when others are competing for the same property. The best approach is to determine ahead of time the maximum price you would pay for a particular property. Be sure to consider all improvement, transaction, and holding costs. Then make a "no regrets" offer. If you win, congratulations. If not, there are plenty more to evaluate and acquire.

Making an offer on a bank owned property can be tricky. Knowin how long it's been on the market is a crucial piece of information for the buyer to have. The fewer days on the market, the less likely the seller is to come off the price.
After all, they've usually had the property appraised or at least have been provided market price evaluations by two local real estate agents. They are pretty confident they have it priced right.
Time will prove them wrong. Until time has proven them wrong, they expect to sell it for at least 90%-95% of list price.
But there are 2 rules about money....
#1. More is better than less
#2. Sooner is better than later.
The IDEAL offer that a bank will receive is FULL PRICE, CASH, WAIVE all contingencies, CLOSE right away.
That is their perspective but it must be a win-win situation for everyone.