What are some of the possible candidates for the ancestors of pterosaurs?  I know that that question has yet to be resolved, but are there any known fossil reptiles that COULD potentially be the precursors to pterosaurs?

I guess here you are asking about possible ancestral forms rather than relatives. As you say, there is uncertainy over this, with most researchers favouring pterosaurs asd being the neareast relatives to the dinosauromoprhs (that's dinosaurs and a few of their basal relatives) and a few people suggesting pterosaurs arose phylogenetically a bit earlier and are buried somewhere in the archosaurs. To put it another way, they either diverged from reptiles after or before the crocodiles.

However, in terms of ancestors, well we don't really talk about direct ancestors-descendents in palaeontology becuase it's imposible to be sure of such relationships. So instead we talk about nearest relatives. For example, Archaeopteryx is not the ancestor of all birds, but it is the closest thing to what the ancestral bird probably looked like. In the case of pterosaurs, there is nothing really which looks that much like a pterosaur but is not one (which is part of the reson that it is so hard to be specific about what they are related two). The nearest thing is the dinosauromorph Scleromochlus, but even this isn't that similar and really just has a few features of the skeleton that link it to pterosaurs - there' not giant arm or elongate 4th finger or anyhting like that. There have been a couple of other suggestions but they are extremely controversial and need serious examination.

In short, not much really, and that's the problem.