I'm not ______ to music at the moment.

The sentence requires a present participle to form the present continuous tense with "am not". Therefore, "listening" is the correct choice. The structure "I'm not listening to music at the moment" is grammatically sound and conveys the intended meaning. The other options, "listen" and "am listening", do not fit the grammatical context of the sentence. "Listen" is the base form of the verb and would require a different sentence structure, while "am listening" would be used in a positive statement or a question, not a negative one with "I'm not".

Final Answer: The final answer is $$\boxed{listening}$$