The report said on Thursday that Mahfouz is no longer taking food, and that his general health has sharply deteriorated.
Egyptian writer Mohammed Salmawi said he is unable to recognise anyone other than his daughters, his wife and his closest friends.
Born in Cairo in 1911, Mahfouz is the author of 50 novels, having begun to when he was 17.
His first novel was published in 1939 and 10 more were written before the Egyptian revolution of July 1952, when he stopped writing for several years.
Mahfouz is best known for The Cairo Trilogy, his saga about a modern Egyptian family living under British colonial rule between the two world wars.
His first three novels – published in Arabic in 1939, 1943 and 1944 – were set in ancient Egypt.
On December 10, 2002, Mahfouz marked his 92nd birthday with an appeal to George Bush, the US president, to lead the world with justice rather than through military force.
On that occasion, the Egyptian newspaper al-Ahram reported, Mahfouz celebrated his birthday at home in Cairo with his wife and two daughters, before going to a party in his honour on a boat anchored on the Nile.