Can I contact a bank before an REO goes on market?

Absolutely. Banks start to accumulate costs, ie.. legal, marketing etc. on REO properties the moment they start advertising their sale so contact prior to that may allow them to sell at a reduced price.

Yes, you can contact them directly but remember that if you purchase the home before auction and the home doesn't sell at auction you will more than likely be able to buy that home for thousands of dollars less than the auction price. Every neighborhood and home is different though. I would recommend hiring a buyers agent (paid for by the sellers/bank) to pull some in depth comps on the neighborhood to get an idea if this property is a great deal or just a good deal. Best of luck. Feel free to contact me if you need a home loan.