Watch the movie “The Man From Earth” for a reasonable exploration of one set of possibilities (Movie on youtube).
Short answer is possible, but not very probable.
It seems very likely that indefinite life extension is possible, and will require some fairly high tech interventions, and should be generally available to all who want it by around 2040 on current trends.
According to a Ray Kurzweil in a livestream interview with Peter Diamandis in mid September 2018 (about 43 minutes into the interview), Ray made two claims quite close together:
“at the end of the 2020s I believe that diligent people will be able to achieve longevity escape velocity” and about 30 seconds later;
“personally I believe that I am diligent enough that I have already achieved longevity escape velocity”.
Longevity escape velocity is the idea that for each year we age, our life expectancy grows by more than a year.