My admittedly limited experience with this subject tells me the following:
Each property and each bank has unique elements, so the process requires you to contact and present a proposal to each holder. Some banks have kept the property "on the books" so as not to show a large loss on their quarterly or annual P&L statements. Some are eager to recoup some money and avoid the hassle, paperwork and sales commission entails in listing the property. Many will want a cash payoff of what they are owed or what they will accept. Some may consider financing your purchase of an REO (earl estate owned) property.
I find most FSBO properties to be over-priced via a vis the market in their area, and you also have to deal with, in many cases, an unsophisticated seller and missing critical disclosures of unknown-to-you items that you would want mentioned in the deal.
If you go the REO/bank route, as you know or can understand, they have oversight committees, departments, auditors and boards looking at the decisions of the officer who decides your proposal, so you will probably need to come to the table equipped with a BPO - broker's price opinion. Ostensibly, it is done by an independent r.e.broker who can justify the price you are offering. It may not be F.M.V but it should not be too distant from that. Depending on what percentage of the property's F.M.V. is owed to the bank, your price offer may be favorably received or not. One option: Seek out a knowledgeable r.e. broker familiar with the process and ideally who had dealt with the specific bank holding the REO property you are pursuing, and ask what his/her expected compensation might be to assist you. It never hurts to have experience in your corner when dealing with monolithic banks.
Some or a lot of this you may already know, but I thought I'd chime in with what I've learned. Using Google to learn more about the process can help you a lot also.