I would like to refer the question to Rabbi Daniel Blass: What is the Jewish view about mermaids? Do they have a soul because they are half human and half fish? How do they reproduce? After all, aren’t they always females? What information is known to us about them? I'd love to hear you explain this in depth. Thanks in advance.
You may have seen images of “mermaids” in the past. These fake pictures were usually dried out monkey organs stitched together with parts of a fish. The first to do this roamed around for many years with these stitched characters, and introduced them in a traveling circus that he founded.
But aside from these fakes, belief in mermaids was widespread in ancient times. Mermaids were supposedly seen by many sailors, and we can assume that in many of the cases, sailors viewed sea cows from a distance (or below sea level), and because of their unique shape, considered them human beings with tail fins. Such rumors also spread based on encounters with distant and strange animals. For example, animals found in Africa have been described in various and bizarre ways by tourists, with the rhinoceros once being described as having iron armor.
In any case, the Gemara does not explicitly mention “mermaids”. The only source which seems to refer to it is where the sages mention dolphins, and say that their reproduction resembles humans’. The tractate of Brachot states (8a): “The ‘dolfons’ reproduce like human beings.” What are ‘dolfons’? Rabbi Yehuda said: ‘Sea creatures.’”
Many, prominent among them Rashi and Tosfos, interpret this Talmud as talking about ‘mermaids’ but they were not referring to speaking creatures with a soul, but only marine animals who externally appear half-human and half-fish. Other commentators interpreted the Talmud on a simpler level, that the Sages in the Talmud were referring only to the dolphins’ behavior which resembles humans in some ways, and not creatures which appear half-human. This is how Rabbi Benjamin Mosfia explained them in his book “Musaf Ha-Aruch” (under the topic “dolphin”): “they give birth to their cubs and nurse them from their teats, and they reproduce like human beings.” Rabbi Jacob Emden (the Ya'avetz), and the author of the Yalkut Shimoni (Genesis 247:31) also explains it this way.
Elsewhere, the sages note a creature living on land that has a human form, which is called “lord of the field” (Kilayim 8:5). There is no doubt that there are very strange creatures in the world, some of them somewhat similar to people, like proboscis monkeys and orangutans.
In the tractate of Chullin (127a), our sages wrote that G-d created creatures in the sea that are parallels to all the creatures on land: “Whatever is in the land – is also in the ocean.” So we shouldn’t be surprised if we one day encounter a sea creature partly resembling a human. So far, they have discovered several species of fish whose shape is reminiscent of a human face.
Even if in the future they will discover a marine species with a human form, this will not be a thunderous scientific finding. After all – there are countless kinds of monkeys that are similar to humans, and countless other creatures that are similar to each other.
Concerning your question, the Torah says explicitly that only humans received a Divine soul, “and He breathed into his nostrils a living soul” (Genesis 2:7), so even if there are creatures in nature that are similar to man (and even appear like “mermaids”), they will not have a human soul.