Pope Francis is fighting pneumonia in both lungs amid fears the infection could spread and cause sepsis.
Pope Francis rested overnight in hospital just days after he was diagnosed with double pneumonia, the Vatican said.
Dr Alfieri said he was highly vulnerable because of his age and general frailty, and warned sepsis caused by the infection would be “very difficult to overcome”.
“Sepsis, with his respiratory problems and his age, would be really difficult to get out of,” Dr Alfieri said on Friday, adding: “He knows he's in danger.
Francis has said he would consider it, after Pope Benedict XVI “opened the door” to popes retiring.