an animal gifted of self awareness and abstract reasoning.

And the word animal implies soul (from 'animus'), it does not deny it.

So if you want you can say souls inside animals, but that's redundant, it's literally the meaning (biology hosting a spirit)

This is also more correct (imo) than saying 'a soul inside an animal' because cultural references aside human is the animal, the soul is the soul and 'human' would therefore be a temporary quality (therefore - animal side)