That report came early Monday morning from officials at Hadassah Hospital, the Jerusalem hospital where Sharon remains in critical condition since suffering a stroke last Wednesday.
Since then, he has undergone two operations to halt bleeding in his brain.
Doctors have kept Sharon in a medically induced coma and on a respirator since Thursday to give him time to heal. Sharon's medical team is now weaning him off the sedatives which have kept him in the coma.
CBS News Correspondent Robert Berger says if Sharon comes out of the coma as planned, doctors will massage and pinch his skin and vigorously rub his chest as they try to determine the extent of brain damage. They will also ask him to perform simple tasks like blinking, moving his arms and legs and talking. Medical experts say Sharon probably suffered some brain damage and paralysis.
Sharon previously experienced a mild stroke Dec. 18.
Sunday, the hospital said a brain scan showed improvement.
Doctors will have no idea how much damage the prime minister suffered until he is out of his coma, reports CBS News correspondent Tony Guida. Dr. Keith Siller, Medical Director at the NYU Comprehensive Stroke Care Center, said it is possible Sharon won't come out of the coma at all.
"Even when the sedation is removed we might not see a significant change in the prime minister's condition" Siller said. "My guess is he'll be in ICU and on a respirator for quite some time."
One of Sharon's doctors has said that the prime minister is unlikely to be able to return to his job and its duties. Acting Prime Minister Ehud Olmert has told the Cabinet he would work to carry on Sharon's political legacy.
The 77-year-old Sharon, Israel's most popular politician, has been viewed by many in Israel as the best hope for resolving the Israel-Palestinian conflict. His grave illness, just three months before elections, has stunned Israelis and left Middle East politics in limbo.
A new brain scan Sunday showed his vital signs, including the pressure inside his skull, were normal, said Dr. Shlomo Mor-Yosef, the hospital director.
"His condition is still critical but stable, and there is improvement in the CT picture of the brain," Mor-Yosef said.
"In light of all these factors, the panel of experts decided to start the process of taking him out of the sedation tomorrow morning. This all depends, of course, on whether the prime minister makes it until tomorrow morning without any significant incidents."
Doctors will pass their assessment of brain damage to Attorney General Meni Mazuz.
"They will inform us the moment they wake him up from the sedation and they will know what systems were damaged and what his situation is," Justice Ministry spokesman Jacob Galanti said.
Olmert is seen as Sharon's potential heir.
One of Sharon's surgeons, Dr. Jose Cohen, said that while the premier's chances of survival were high, his ability to think and reason would be impaired.
"He will not continue to be prime minister, but maybe he will be able to understand and to speak," the Argentina-born Cohen said in comments published Sunday by The Jerusalem Post.
Outside experts were even less optimistic.
"There is zero expectation on my part that he will have the capacity to perform in any kind of formal way," said Siller.
"We are basically hoping he survives and that he has some kind of ability to get some rehab so he can have some useful function again. But we are talking about the basics, we are talking very basic things. The complexity of this man, and what he did for a living, this is not to even be considered now. This is absolutely unrealistic at this time."
Israel's Cabinet met for its weekly gathering Sunday for the first time since Sharon's stroke.
Olmert sat next to Sharon's empty chair, the prime minister's untouched gavel rested in the middle of the table.
Olmert told the ministers that Sharon would want everyone to get back to work on the country's pressing security, social and economic issues.
"This we will continue to do," he said. "We will continue also to carry out the wishes of Sharon, to manage affairs as necessary."
The Cabinet meeting was Olmert's first formal opportunity to persuade Israelis and the world that the nation's affairs were in good hands and that he would pursue Sharon's political program.
Shimon Peres, the Labor Party elder statesman and Nobel Peace Prize laureate who abandoned his party to join Sharon in Kadima, dispelled rumors that he might return to his former party or challenge Olmert. Addressing a gathering in Jerusalem on Sunday, he said he "fully and faithfully" supports Olmert. Later, in a CNN interview, he called on his backers to vote for Kadima.
Speaking to reporters later, Olmert expressed hope Sharon would get better.
"I pray with all the people of Israel that my tenure as acting prime minister will be short, so soon enough we will be able to see again the leader of Israel," he said.
Before his collapse, Sharon appeared headed to a landslide victory in March 28 elections as head of his new centrist Kadima Party, formed in the wake of his withdrawal from Gaza this summer. Sharon was expected in a third term to try to draw Israel's permanent boundaries, evacuating small West Bank settlements while strengthening Israel's hold over larger ones.
But it is unclear whether Olmert or any other successor would have the popularity or charisma to carry out such a plan.
Sharon had been reluctant to resume long-stalled peace talks, saying the Palestinians were not a trustworthy partner.
In the West Bank, Palestinian Prime Minister Ahmed Qureia wished Sharon a quick recovery and expressed hope for new peace talks.
"We are looking for a new era in which we can negotiate and be partners in a real peace that serves both peoples," he told his Cabinet.