The two knobs on my radio are very sticky. I tried something gentle, Sprayway and a tooth brush, so as not to affect the painted parts on the face of the dial with no result - still sticky. I bought the car this way so I don't know what or why it's sticky.
What kind of car is this? Hard to say when we have no clue what the knob is made of etc. Maybe a picture would be helpful too. Most times the knob will just pull off then you can clean it without worrying about the surrounding areas.