I'm sure it depends on the animal. In fact humans think in at least two inner voices.

The ear consciousness is receptive, and the speech consciousness is active.

What I mean by this is a dog or another animal that spends a lot of time with people likely has a passive inner voice of their owner. A dog might hear an owner yell no when they go to do something the owner doesn't like, even if their owner isn't around.

Animals that are capable of speech such as a parrot, will likely have an active speech consciousness. Which is more somatic in tone.

For example, when I am in active speech consciousness I can feel my jaw and tongue muscles move. When in passive listening consciousness, my ears might move or strain to try to hear the inner speech.

With practice these somatic sensations can be decoupled from their internal sense consciousnesses. Which tends to help them quiet down and deepen meditation.

This is one of my favorite practices that's accessible for people who don't really meditate. The guided meditation is the first fifteen minutes of the video, so you don't have to listen for the whole hour to get an inkling of what I'm pointing at.

https://www.youtube.com/watch?v=7OW9LNSVjPo