There is no single word that means this.
To say that somebody is close to being dead means that their life could end very soon, but with luck or care they could recover instead. The only ways to say this involve more than one word, usually 'near death'; you may have read of the fascinating experiences some people have had when near death, people who survived to tell their story.
Alternatives such as 'almost dead', 'half dead', 'nearly dead', 'all but dead' can be used, but they are more frequently used as an exaggerated way of saying 'feeling bad', perhaps after climbing the stairs too quickly. This overuse can rob them of the seriousness that death deserves.
'Dying' is a single word, but to say somebody is dying means that they will certainly die, maybe soon or, in the case of some illnesses, after several years. There is no sense of closeness in the word 'dying' itself, though often this is clear from the context, as in Su.Ki's example.
Strictly, the single word 'moribund' means 'dying soon', so it doesn't quite fit. Worse still, the word is nowadays always used metaphorically - e.g. to describe the state of a decayed town - and without any sense of closeness or certainty, it is just a long, fancy-sounding way of saying 'dilapidated' or 'run down'.
'As good as dead' means under threat of death, for example if subject to a fatwa or Mafia contract.
'One foot in the grave' is a disrespectful way of saying 'very old'. This is close to death in a very specific sense, perhaps not the one you intended.