Doesn't matter. Even if they have souls, humans have dominion over them.
Genesis 1
28 God blessed them and God said to them: Be fertile and multiply; fill the earth and subdue it. Have dominion over the fish of the sea, the birds of the air, and all the living things that crawl on the earth. 29 God also said: See, I give you every seed-bearing plant on all the earth and every tree that has seed-bearing fruit on it to be your food;
30 and to all the wild animals, all the birds of the air, and all the living creatures that crawl on the earth, I give all the green plants for food. And so it happened.
31 God looked at everything he had made, and found it very good. Evening came, and morning followed—the sixth day.
Genesis 9
1 God blessed Noah and his sons and said to them: Be fertile and multiply and fill the earth.
2 Fear and dread of you shall come upon all the animals of the earth and all the birds of the air, upon all the creatures that move about on the ground and all the fishes of the sea; into your power they are delivered.
3 Any living creature that moves about shall be yours to eat; I give them all to you as I did the green plants.
But, there are animals in heaven
Isaiah 65
17 See, I am creating new heavens and a new earth; The former things shall not be remembered nor come to mind.
…
25 The wolf and the lamb shall pasture together, and the lion shall eat hay like the ox—but the serpent’s food shall be dust. None shall harm or destroy on all my holy mountain, says the Lord.
Rev 19
14 The armies of heaven followed him, mounted on white horses and wearing clean white linen.