I'm torn on this. I've been digging around looking for confirmation one way or the other.
As a rule, I treat sleeping individuals as having the Unconscious condition which makes them auto-fail dex/str saves. Also makes attacks against them have advantage and such. That doesn't appear to offer any specific protections or weaknesses to Charm, nor does the Incapacitated condition, which Unconscious automatically imposes.
I would think, per RAW, yes even asleep you are susceptible. If you would prefer, Cosmic, we could rule that this item RAI requires the target creature to be conscious at the time they are meant to be charmed. I leave it to you.