Give it a shot. Banks' motivations change. Maybe it wasn't motivated before, and it is now. Maybe potential buyers have been listening to the naysayers (including some below) who wonder why a bank would accept a low offer. And you can be pretty much confident that, despite what's written below, there aren't 20-30 people competing for the same house. Otherwise, it'd be long sold.
Sounds like you've done your initial homework regarding preapproval and knowing what was owed to the bank. Now what you've got to do is find out what the home is worth on the open market. You can figure it's not worth $325,000, or it would have sold. You already know that. But what are the current comps? The point to this step of the exercise is to make sure you don't overpay. The bank should have some idea of what it's worth--it probably had a BPO (broker's price opinion) done on it. And they'll know, too, that it's not worth close to $325,000.
Problem is, some banks like to hold on to property if they think the market will recover fairly soon. That way, long term, they can cover their losses. On the other hand, sometimes they want to clean up some of their non-performing loans, so a non-motivated lender a month ago may be motivated now.
Bottom line: Determine the comps. Make an offer that does not exceed the comps (and probably should be comfortably under, since prices probably will continue to decline for awhile), and that is under your pre-approved limit.
Hope that helps.