If jellyfish are capable of thinking, then it could be said that they possess a mind. For many philosophers and theologians, the term mind is synonymous with the term soul. Consequently, it could be argued that jellyfish have souls. Now, this might seem like a very strange thing to claim. However, such a claim is not necesarily foreign to Christian belief. In fact, it can be argued that such an idea is quite biblical. As Christian philosopher J.P. Moreland explains:
It is sometimes surprising to people to learn that the Bible teaches that animals, no less than humans, have souls. In the Old Testament, nephesh (soul) and ruach (spirit) are used of animals in Genesis 1:30 and Ecclesiastes 3:21, respectively. In the New Testament, psuche (soul) is used of animals in Revelation 8:9. Moreover, it is a matter of common sense that animals are not merely unconscious machines. Rather, they are conscious living beings with sensations, emotions (like fear), desire, and, at least for some animals, thoughts and beliefs. The history of Christian thinking is widely united in affirming the existence of the "souls of men and beasts" as it has sometimes been put...(The Soul: How We Know It's Real and Why It Matters, p. 141).
However, in suggesting that jellyfish have minds or souls, I am not asserting that the thinking of a jellyfish is similar to that of a human. For his part, Moreland argues that "...we should attribute to animals by analogy [to humans] those [mental] states that are necessary to account for the animal's behavior, nothing more and nothing less" (The Soul: How We Know It's Real and Why It Matters, pp. 141-142). Consequently, using this approach, we will find that as we "move down the animal chain to creatures that are increasingly unlike humans--from primates to earthworms--we are increasingly unjustified in ascribing a mental life to those animals...All living animals have souls if they have organic life, regardless of the degree to which they are conscious, but we are justified in attributing less and less to the animal soul as the animal in question bears a weaker analogy to us" (The Soul: How We Know It's Real and Why It Matters, p. 142). Therefore, since jellyfish would seem to be closer to earthworms than to primates on the animal chain, it is most likely that their mental life is quite limited.
In short, while it may seem bizarre to assert that jellyfish have souls, the scientific and biblical evidence would seem to favor such a claim. Nevertheless, per Moreland, the significance of having a soul is much less for jellyfish than it is for humans, who alone are created imago Dei--in the image of God.
Image of a jellyfish from Wikimedia Commons