As I am applying/talking to potential supervisors is it appropriate to mention (but not elaborate) that I have a paper under review at a specific conference? Or would this be a potential breach of double-blind process of the conference?
I would not mention the paper's name, but perhaps the areas the paper is related to
That should be fine. You might get asked for a copy of the paper in which case a conversation might be needed. If the professor isn't a reviewer for the conference then sharing it should have no effect.
But showing some research output is a good thing in approaching a potential advisor.
The information that you have an unnamed paper under consideration doesn't break the double blind process.
