I have some initial conversations related to the scope of the research area with my potential supervisor. I took a course with him as well. He knows me well too. I asked him to supervise me in my first e-mail. He did not tell me his opinion though. However, I am not sure he will take me or not as thesis student. How can I ask him politely to know about his consent to supervise me? I appreciate your help!
You don't need any special wording or "politeness" beyond what is normally expected of adults. Tell him that you would like him to supervise you and that you are interested in the research area you discussed. Ask, explicitly, if he is willing and able to take you on.
If there are other considerations, such as funding, that he controls you will have to bring that up, of course. In the US, doctoral student funding is normally handled at the department level, though there are exceptions in which a professor funds students from grants. If you aren't sure, ask.