How do we define "suffering"? Is it the same emotional experiences we call "fear" and "sadness", i.e., the ability to have the concept "I am afraid/sad"? That means the animal needs to at least have a primitive form of understanding and introspection to qualify (e.g., great apes, chimps, bonobos).
If we go to the other extreme, we must admit we don't have a reliable method for communicating with animals (famous "dog whisperers" aside). We can only infer "suffering" is taking place when the animal reacts negatively to a negative external stimulus. But bacteria respond negatively to a negative external stimulus as well. Sure, there's mind-bogglingly more complexity in a mammalian brain than a bacterium, but if we reduce "suffering" to the observation of a negative reaction to a negative external stimulus, we must say even single cell organisms are "suffering."
Hard to strike the right balance.