Good morning Rich,
First, any Realtor worth her mettle would NEVER take a Buyer out without knowing the Buyer is prequalified for mortgage financing. What you're asking in your query is this: "Where can I find the least experienced, least professional real estate agent who will allow me to waste his time and in turn will waste my time?"
Line up your mortgage financing and connect with an experienced real estate pro, the kind who says, "I'm sorry, I don't show ANY houses until you've been Prequalified for a mortgage."
Second, simply because you've got a home that is on the market does not make you any more qualified than another buyer. In fact, you're probably LESS qualified because you have to sell in order to buy. Many homeowners are reluctant to enter into a transaction with a Buyer who needs to sell in order to buy.
Get prequalified and let your Mortgage Banker guide you on what you can and cannot do to move forward on buying your next home.