No. Obviously the human soul isn't compatible with an animal body. A soul can only reincarnate in its compatible body and there are differences in souls. Not even a gentile can reincarnate into a jew or vice-versa unless there's an exception and Satan intervenes (see Anton Lavey, he had a gentile soul but he was incarnated as a jew to promote Satanism in a jewish controlled world which he would have failed if he was a gentile).