Generally, you should be eligible for a mortgage 2 years after a short sale. You'll want to check with a lender for the specifics and requirements. Next, if you want to buy the house you are renting - the owner will have to A. "want" to sell it, and B. "be able" to sell it. If there is a sizable loan outstanding on the property, the owner may be renting it out because he/she can't sell it for enough to satisfy the remaining balance.
Regardless of if you convince the owner to sell you the property you are renting, you'd still have to qualify for and obtain the financing (unless the owner will finance you) to ultimately pay for it. Hope that helps!