murmur at (one)
To mutter or whisper (something) to one. A noun or pronoun can be used between "murmur" and "at" to specify what is being said. She kept murmuring at me throughout the car ride so her parents wouldn't hear her, but I couldn't hear her either! I could hear two students murmuring at each other at the back of the class.
murmur at (someone or an animal)
to say something softly or indistinctly to someone or an animal. Stop murmuring at me. Speak up! Gene sat alone, murmuring at his favorite cat for over an hour.