The 77-year-old premier reportedly blinked his eyes on Monday after family members played a tape of his grandson’s voice.
A spokeswoman for Hadassah hospital, where Mr Sharon has been treated since he suffered a massive brain haemorrhage on January 4, said the medical significance of "eyelid movements" was unclear.
"He blinked -- both eyes -- but the medical significance of this is not clear," Yael Bossam-Levy said. "Only the family saw it, no doctors were in the room."
A report on Y-net, the website of Israel's top-selling Yediot Aharonot newspaper, said doctors rushed to Mr Sharon's room after being alerted of the movement but that the prime minister's eyes were shut when they arrived.
It was the first time Mr Sharon has shown any movement in any part of his eyes since he was first admitted to hospital and placed in an artificial coma.
On Sunday, doctors performed a successful tracheotomy on Mr Sharon in order to assist his breathing, before returning him to the hospital's neuro-surgical unit.
Doctors have been unsuccessful so far in rousing Mr Sharon since reducing, and then on Saturday stopping, sedatives used to induce a coma aimed at stopping his brain from swelling.
Medical sources have been increasingly pessimistic about Mr Sharon's chances of recovery the longer he remains in a coma.
Doctors said his conditioned remained "serious but stable".
Parties prepare
In a sign that Israel was moving quickly to fill the political vacuum left by Mr Sharon, his new Kadima party named interim Prime Minister Ehud Olmert as acting chairman to lead it into a March 28 general election.
"Olmert has been officially appointed as the interim leader of Kadima until Prime Minister Sharon's health allows otherwise," party spokeswoman Maya Jacobs told news agency AFP.
Attorney General Menachem Mazuz declared on Sunday that Mr Olmert can continue as Israel's acting premier until the March 28 general election if Mr Sharon remains incapacitated.
Mr Olmert was due on Wednesday to seek government approval for four new ministers.
Mr Olmert has announced replacements from within Kadima for four Likud cabinet ministers who quit over the weekend.
In the most high-profile appointment, Justice Minister Tzipi Livni, widely seen in Israel as a rising political star, will become foreign minister replacing Likud’s Silvan Shalom.
Opinion polls predict that centrist Kadima, which Mr Sharon established after quitting the right-wing Likud in November, will easily win the election with Mr Olmert at its head.
Meanwhile Likud leader Benjamin Netanyahu has been appointed opposition leader.
Mr Netanyahu last week instructed the four Likud members to quit the coalition government to enable Likud to campaign as an opposition party.