You are correct that normally banks do not accept a contingency that requires the buye rbe able to sell their current property first. This is even more true in the current market with the banks having so many foreclosed and repo properties to deal with and with times on the market to sell properties being longer.
In your situation, if you are really intent on purchasing the bank owned property, you may want to explore using a bridge loan. You can read about them here: http://www.brianwess.com/NeedaBridgeLoan
If you would like I can also refer you to some professional local lenders who can discuss bridge loans, how the work and their requirements with you.
It is great to be excited about a good deal, but don't overextend yourself to get the home. You can check with a lender to see what options you have, but keep in mind that your home may take longer to sell than you think. Have your Realtor explain the average days on market for your neighborhood and the market value of your home. Good luck!