My Father’s Dragon by Ruth Stiles Gannett

One cold rainy day when my father was a little boy, he met an old alley cat on his street. The cat was very drippy and uncomfortable so my father said, “Wouldn’t you like to come home with me?”
This surprised the cat—she had never before met anyone who cared about old alley cats—but she said, “I’d be very much obliged if I could sit by a warm furnace, and perhaps have a saucer of milk.”