Genesis makes no such statements about man's physical body.
Man WAS originally designed for death, and I think that I can prove it. All one has to do is wonder why the tree of life was in the garden. But I have to ask you, why have a tree in a garden of which you can eat and that will cause you to live forever if you are able to live forever without it. I would therefore argue that Adam would have lived forever, if and only if, he had continued access to the tree. Nowhere do we read that the animals ate from the tree.