Yes, prevention of aging is within our grasp - in the sense that a package of foreseeable medical technologies could enable repair of the low-level biochemical damage that causes aging, and those technologies might take only twenty years or so to develop. Unfortunately, that timeline is dependent on a large amount of funding and a dedicated research community, neither of which presently exists for many of the essential parts of this research program. While the regenerative medicine and cancer research communities are populous, well funded, and achieving progress, very few researchers are presently working on other goals necessary to halt the aging process - such as repair of mitochondrial DNA.
So when I say "within our grasp," I mean "if we all get up and do our part to make it happen." It takes a wave of public interest and advocacy to steer the scientific community and large funding institutions - and they presently need steering towards repair-based strategies to deal with aging, otherwise the first working rejuvenation therapies will arrive too late for those in middle age today.
Here is an article from Ageing Research with a different take on "within our grasp":
Slowly but steadily knowledge about the human body has progressed and new ideas of animal ageing have immerged. The classic model of ageing, based on "accumulation of errors" has become an outdated notion. Instead, evidence suggests that ageing, at least in part, is likely the result of a failure in the function of cells (such as stem cells) required for cellular regeneration. Replacing impaired stem cells with fully functional stem cells should thus prevent/treat age-associated pathologies allowing us to live healthier longer lives.
This sort of viewpoint I see as a dangerous path of complacence. While it is true that (a) regenerative medicine and stem cell science are racing ahead, and (b) the ability to replace tissue, whole organs, or damaged stem cell populations will do much to help, you can't fix aging with stem cells alone.
I've had to make this point with a number of folk who are enthusiastic about progress in regenerative medicine and think that it will enable great extension of human life. Unfortunately this is not the case, as a great deal of degenerative aging is built atop a build-up of waste biochemicals and the body is an integrated system - the health of each of its subsystems impact the others. You can't fix problems in isolation; you can't drop new stem cells into age-damaged stem cell niches, and you can't put a new heart into a body with corroded arteries and expect it to be just fine. If you replace some failing tissue with fresh tissue, that fails to solve a range of other eventually fatal problems.
This is another aspect of the well known factoid regarding cancer research - if you cured cancer and made no other advance in medicine, that state of affairs would add only a couple of years to overall human life expectancy. The people who survived cancer thanks to the miracle therapy would soon be cut down by other conditions of aging. All of the life-span-limiting forms of biological damage have to be repairable before we can greatly extend our lives. There are no short cuts: it doesn't matter how well regenerative medicine is progressing, the other branches of longevity science must also progress rapidly if we are to live longer.
Given that those branches are for the most part not well funded, nor the focus of large and vigorous research communities, this means that we have work to do.