I'm sorry I can't provide any other details

You possibly can with some local research of your own. Many educational institutions traditionally retain images of their famous alumni, plus other significant local exemplars. If you know the image was displayed in a professor's office, you presumably know details of both the institution and the department. Additionally, large institutions tend to compile inventories of all their property, so it may be recorded on a central registry as part of that institution's housekeeping. Even if the current professor inherited their office's decor, some associates of the previous incumbent may still be around. Good luck.

Most likely, it's a photograph from a family or individual collection from the 19th Century, although it may certainly be someone notable in a particularly locality. There are a lot of portraits like this around with no context as to who the people in them are; the Arabella Chapman Project is an attempt to catalogue one such collection of photographs. You can find many more photographs like this in this digitised collection by the Schomburg Center for Research in Black Culture, if you look at their Portraits section. As /u/PlazaOne says, asking around your institution is probably your best bet for getting an answer.