The 85-year-old has been in a coma for almost eight years after suffering a stroke in January 2006.
Now doctors at the Tel Hashomer hospital say his health has declined to a "critical" condition.
Sharon's family is at his bedside. One of his sons told the Jerusalem Post, "We have hope, we always have hope."
Sharon was first elected prime minister of Israel in February 2001.
His complicated legacy is still being debated in Israel, where he was known as a celebrated general and a politician nicknamed "the bulldozer" for his ability to push through his political agenda. The Arab world knew him as "the butcher of Beirut" after he, as defense minister, orchestrated Israel's 1982 invasion of Lebanon, an effort aimed at Palestine Liberation Organization fighters, but that also left hundreds of Lebanese civilians dead.
Despite being known as the father of the Israeli settler movement, in 2005 he ordered the withdrawal of all Israeli troops and settlers from the Gaza Strip, and several West Bank settlements.
He left the right-wing Likud Party that year to set up a new centrist party, Kadima, but suffered a stroke a year later, whereupon he slipped into a coma.