With home prices so low, have you considered buying instead. You monthly payments could be less than what you pay in rent now.
But if you insist on renting, perhpas you could ask the landlord to give YOU a copy of his credit report to see if HE is current on his mortgage. Reverse qualification if you will? :-)
Remember, if the property sells as a short sale, the new owner will have to adhere to the terms of your lease. Most likely you will have a month to month lease allowing for the the current owner to provide you a 30 day notice once the lender approves the short sale. If the property goes to trustee sale, your lease will be void, which means you would be required to move out of the house immediately. Not a good positiion to be in.
I don't know if it's a wise choice to rent a home in this situation, unless you are getting a great lease price.
What will be the terms of your lease contract? Is the new owner going to require you to move, or will be willing to rent you the property once they buy it? Have the short sale been accepted? Have the owner received already a Notice of Trustee's Sale, if so when is the sale scheduled for?
To give you the right advise we will need more information as you can see. But generally it will be a very bad idea to rent a property that is currently listed as a short sale. Unless you are ok with staying there, potentially, a very short period of time. They might have an acceptance in two weeks, or it might take 6 more months - of the foreclosure sale might be scheduled for next month. It will all depend.
Remember that the big majority of short sales never close, which means that there is a good chance that they property will be foreclosed and most probably you will have to move by the date of the foreclosure date to avoid being evicted.
Good luck, and think if twice before renting a short sale property unless you are aware of all the details and potential consequences.