It is possible to rent then purchase. If it is a all negotiated up front, it is called a lease option. However if you rent a home now, you can approach the owner at a later date and express your interest in purchasing the home at that time.
It is possible the owner would let you rent and sell it later to you if you can obtain a loan to buy it. No loan means you can't unless they do the financing for you. Do a search of Land Contract and Rent to Own.