You appear to be looking for not just a rental home but a home that you can rent with the intention to purchase. These situations are quite rare and also complicated. Most rental home owners are investors who are seeking to make a bit of profit on their investment and do not wish to sell.
If you do find an owner willing to lease and sell later as part of the agreement, the rent-to-own contractual agreement should be written by an attorney to protect the interests. In addition, as part of this contract, the Tenant pays more than the fair market rental amount in order to warrant the Seller commitment to sell them the property even though the market value may raise (as expected will happen) over the term of the rental agreement. The rent-to-own concept was more popular several years ago when the Sellers were having challenges finding Buyers. That situation is changing.
Feel free to contact us. Good luck with your search.