I concur with Paul in emphasizing the importance of being VERY careful. Is the property in pre-foreclosure status? Has a Notice of Trustee's Sale been filed? What are the owner's plans and intentions? etc., etc. If the house is listed in MLS, I would probably also talk to the Listing Agent and see what s/he knows about the situation. It's risky business!
Yes, you can rent a home while it's listed as a short sale. But be careful! Your deposit may not be safe and when the property transfers owners, either back to the bank or sold at auction, you will be eventually evicted. Be careful. You also want to make certain that the person renting the house to you is the actual owner or has the legal right to rent the house. A lot of renters are being taken advantage of. So, don't become another statistic.
What you need to do is to have a licensed REALTOR assist you, to make certain that your deposit is safe and that the person renting the house to you is either the legal owner or has the right to rent it. But yes, it is possible to rent a short sale.
Buyer's Agent REALTOR