In "The Love Song of J. Alfred Prufrock," T. S. Eliot uses figurative language to describe the yellow fog in terms of an animal, most likely a cat. He does not use simile or direct metaphor to explicitly say that the yellow fog is a cat or is like a cat, but the language he uses to describe the behavior of the fog is language we might more usually associate with a cat.
Certainly, the fog is described as being animate. It can perceive the world around it—"seeing" that the night is soft, the fog curls itself around the house and, like a living thing, falls asleep. Some of the terms used to describe figurative parts of the fog creature are also terms we would apply to cats, such as the emphasis upon its use of its tongue. When we imagine the fog rubbing its metaphorical "muzzle" against window panes, "slipp[ing] by the terrace," making "a sudden leap," and then eventually settling itself down to sleep, we picture it as an animal, something spry and familiar with the environment it inhabits. While the fog is not directly compared to a cat, most readers will likely think of a cat, given the characteristics that Eliot evokes.