While you can always try and put in an offer with a contingency, the likelihood is that the bank will not accept this offer. The bank is not in the business of selling houses, they want the property off their hands as soon as possible for the best price possible.
When given the option between an offer that is all cash and one that is contingent on getting a mortgage, the homeowner will likely choose the cash offer even if it is for a bit less then the offer contingent on the mortgage. This is because the offer accepted by the homeowner must then be accepted by the bank. The key to short sales is closure. The homeowner doesn't want to get to the point of foreclosure so they want an offer that is certain. When there are contingencies nothing is certain, especially in this market.