In my opinion, immortality would never be possible. However, in case medicinal technology learns how to grow new organs such as liver and heart from existing genes, then perhaps living forever could become possible.
Nevertheless, it would not be possible for humans to stay on earth forever since after a billion years or so Earth won’t remain habitable for life. In that case, even if humans manage to stay alive forever, they will have to reach out to other habitable planets to form colonies so as to continue the race. Otherwise, humans are destined for their ultimate demise as a race anyway.