The most probable answer is the bank is going to send you packing. Keep in mind they know what the house is worth based on current market conditions and they most likely already know what they are willing to accept. Their business is finance and they wouldn't be in it for long if they didn't know what their investments were worth, even the ones they are going to write off as a loss.
Your best bet would be to have your realtor do comps in the area and a reasonable offer would be somewhere around 6-10% below market value. I'd be interested to hear if you even get a response from the bank. Bear in mind that once they have already assumed the cost of a foreclosure and the home didn't sell at auction; they are going to try and recoup as much of their cost as possible.