No. 1.) A sale implies transfer, and you can't transfer something you already own to yourself. 2.) Your mortgage lender has to approve a short sale, not only will they not approve you but they won't approve a short sale for a 'non arm's length transaction'. This is the lending term for a sale between two interested parties (parent to child, relative to relative, etc).
What you can look to do is approach your lender about a loan modification. If you get approved for a modification they may lower your principal balance (what I assume you are looking to do via a short sale). The only downside with this is that lenders will typically want proof you are having difficulty making the payment to modify your loan, a loan modification will also negatively impact your credit as you are modifying the terms that you agreed to on your loan.
AC