Quitclaim deed with mortgage attached...advice please

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Hello BP, I am new to this site and have a question or asking advice I should say. I know there are a lot of knowledgeable members. My wife and I have come into a situation where we are looking to gain a single family house via quitclaim deed from parents. It was a rental for them and would be for us as well. There is a mortgage. Our plan would be to continue making payments while the mortgage remains in their name. And later hopefully refi and pay a certain amount to our parents. I’ve heard a bank may refi even without 20% down payment if you can show the deed is under your name and you have been making the payments. We currently own a home and it would take a long time to save down payment. Does this sound like a possibility?