The 88-year-old pope has been treated for double-sided pneumonia since February 14. The situation has occasionally been described as critical and he has needed to be on a respirator on several occasions.
But a few days ago, it was announced that the pope had started responding to treatment and had had "a gradual, small improvement". And on Tuesday, it was reported that the pope had had a calm night and that discharge may become possible in the future.
"The Holy Father's clinical condition continues to be stable", according to a statement from the Vatican.
The head of the Catholic Church still requires hospital care for several days, according to the doctors. He receives extra oxygen during the day and uses a breathing mask at night.
The pope is frail and has previously had recurring bronchitis and other respiratory problems. He is missing a part of one lung after an infection that nearly cost him his life in the 1950s in his home country of Argentina.