Question on etiquette while trying to secure a postdoctoral position Let us suppose that a certain senior Ph. D. student is interested in "securing" a postdoctoral position under a professor whom he does look up to. Would it be right for the student to write the researcher and ask him if he stands a chance of eventually being hired as a postdoctoral fellow in the institution wherein the researcher works? The Ph. D. student is certainly interested in some topics on which the researcher has written in the past; furthermore, there is a certain problem at which the student plans to try his hand once he manages to graduate and this problem is also somewhat near the area of expertise of the researcher in question.

Thanks in advance for any suggestion you may want to leave for me below.
How close are you to graduating? If you're still a few years away, then perhaps get an introduction from your advisor to that professor and see if there are natural ways to seek feedback or advice from that professor. 

If you are thinking about the next year and a half, then your questions should be more concrete. In particular, you might tie your question to funding, as that determines a lot of the possibilities. Even if a professor loves your work, they can't hire you if they don't have the money for it.


If you see from the professor's CV that there is an active grant, you could ask about whether there is space on that grant.
If there are regularly postdoctoral openings in the person's department, you can ask about whether the professor is looking for another postdoc soon. (You may learn that people in the department tend to take turns hiring postdocs, and the professor is (un)likely to be up this year. Apply anyway, but know your odds.)
You could say that you're preparing to apply for an external grant for a postdoc (e.g. NSF in the U.S.) and wondering whether the professor would be open to having you work with them on that. (Often a faculty sponsor is already required to apply.)