Are you limited to the interests of the professors or your advisor during graduate research?
Say you're a professor reading the application of a prospective student who wants to work on topic X, which is not your specific interest (your interest is Y). You may be thinking along any of the following lines:


"I'm doing Y, and I have lots of interesting research ideas around Y. I want students to help me explore these ideas in Y, so I won't supervise a student in X."
"I'm doing Y, and I can supervise students in Y reasonably well. But supervising a student in X for the first time would require a substantial extra investment of time and effort on my part, and I'm not able to offer that right now."
"X is really interesting. It would be useful to develop expertise in X. But currently I only have funding for Y (and PhD offers in our field are always funded), so I can't take on this student unless they are fully funded by an external fellowship."
"X is really interesting. It would be useful to develop expertise in X in this research group. I'll take on this student even though I have no interest in or expertise in X." But then this advisor may turn out to be an ineffective advisor for this student.
"X is really interesting. I don't have any expertise in X specifically, but I do know about the closely related field Y, and I think this expertise would enable me to effectively supervise a student in X, so I'm willing to take on this student." (It may or may not turn out to be true that expertise in Y will translate to effective supervision in X.)
"X is a major up-and-coming topic, which is why I just hired that postdoc with expertise in X to start this fall. With her help, we could definitely get a PhD student started in X."
"I wouldn't take on a student whose main topic is X, because that's not my primary research interest. But if the student was working on my topic, Y, I would be open to also pursuing X with him as a side project."


Since you don't know which of these apply, if you contact this professor, it would be a good idea to indicate that you would be very happy working on Y (if that's true) in addition to your interest in X.