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.