This is a very common question.  The short answer is "no" and here's why: 

A time share by definition is a "shared" or part-time membership to the use of real property - namely a vacation condo unit or hotel suite.  A purchase of a time share is essentially a lessee agreement and not a "true" ownership or real property.

Second, the fundamental purpose of a short sale is the avoidance of foreclosure, thereby selling the property at a value or price that is less than what is owed on the mortgage.  In order for a short sale to take place, you must be a borrower named on the note and the deed to the property; not meeting these two conditions you do not have grounds for a short sale.

In theory, sure. Short selling a time share property is similar to short-paying or "settling" any debt (mortgage, credit card, personal or car loan, etc). Unfortunately, due to a number of factors, a lot of borrowers and creditors are finding themselves in a position requiring settle accounts.

You are asking the creditor or lienholder to accept a lump sum payoff of the debt for less than the amount owed. The lienholder (bank of servicer) is generally willing to do this only if they see it as the only solution . . . the property or collateral is not worth as much as is owed ( it is "underwater"), and you have been proven unable to make the payments. Note that, just as when any creditor short-settles a debt, your credit will likely be affected. You will not be allowed to profit from the - any proceeds from the sale will go directly to the bank or lienholder. You will need the lender's permission to move forward.

If you are unable to make the timeshare payments, contact your lender for information about resolving the issue. Be prepared to show bank statements, paystubs, etc. to prove your inability to pay, and if you can, something that suggests that you would be unable to sell the property for the full amount owed.

Best of luck!