sharp-eared; quick to catch rumors; keen-eared
Describes a person who is unusually quick to hear gossip, secrets, or rumors, often with a slightly negative or wary nuance. Used as a noun or noun-like expression.
He has sharp ears, so be careful with secrets.
My sharp-eared colleague quickly caught wind of the rumor about me.
retentive memory for heard things; never forgets what one hears
Refers to the ability to remember everything one hears, often with a sense of amazement or caution. Less common than the rumor-related sense, but still used in everyday speech.
My grandmother has an incredible memory for things she hears; she never forgets a story once she's heard it.