It could mean: 1. The person's voice doesn't sound the same as yours. Example, someone says you sound like Justin Bieber when you sing, but you disagree, so you say "He doesn't sound like me." 2. Certain actions, behaviors, or words do not resemble your own. For example, you and your friend get drunk on the weekend. Your friend says you were loud, flirting with every girl at the bar, and throwing up everywhere. You say "I don't remember. That doesn't sound like me."

Thank you everyone

I agree with N. You need to give context. It could mean any of the three things he suggested.

Context? The sound does not sound like me speaking? The things you are saying do not sound like anything that I would say. The behaviour you are talking about does not sound like anything that I would do.