A unilateral ceasefire would allow Israel to avoid agreeing concessions with Hamas, such as easing the 18-month-old blockade of the Gaza Strip, which has prevented medical aid and basic supplies reaching the Palestinians.
Al Jazeera's Alan Fisher, reporting from the Israel-Gaza border, said that a unilateral truce would play well to the domestic audience as parliamentary elections approach.
"The Israeli government can say there was no deal with Hamas, they are not doing this as part of any negotiations with what they regard as a 'terrorist' group," he said.
An unnamed Israeli official told the AFP news agency that Israeli troops would remain in Gaza in the event of any such ceasefire being called.
"If they [Hamas] decide to open fire, we will not hesitate to respond and continue the offensive," the official was quoted as saying.
Israel's stated aim of the war, which it dubbed Operation Cast Lead, was to halt Palestinian rocket attacks on southern Israel.
Egypt has been pushing Israel and the rival Palestinian factions to reach a deal that was expected to see an immediate ceasefire and an agreement over security arrangements for Gaza's crossings.
A Hamas delegation from the Syrian capital, Damascus, arrived in Cairo on Friday for a second round of talks on a ceasefire proposal.
Their return followed a meeting between Amos Gilad, a senior Israeli envoy, and Omar Suleiman, Egypt's intelligence chief.
Earlier this week, Hamas proposed a one-year renewable ceasefire in return for an end to the Israeli blockade, which has been in place since the group seized full control of the Gaza Strip in June 2007.
"We want guarantees that the crossings will remain open. If Israel accepts the principle of guarantees, then we will start talking about their details," Osama Hamdan, a Hamas official in Beirut, said.
Marwan Bishara, Al Jazeera's senior political analyst, said: "We have seen unilateral moves by Israel, whether it be in Lebanon in 2006 or Gaza in 2005.
"Those unilateral decisions simply compound the problem, simply delay the problem, but they never resolve the problem.
"I think this is because Israel has run out of options. It realises Israel couldn't deliver what it needs, Hamas wouldn't agree to its conditions and it realises more of the same, the same shelling, the same bombardment ... is making people in Israel think twice about how to continue."
However, as reports of the possible ceasefire emerged, the Israeli military continued to pound the Gaza Strip.
At least 10 people attending a funeral wake died when Israeli forces destroyed a house in Gaza City.
|At least 1,155 Palestinians have been killed during the 21 days of Israel's offensive [AFP]
Earlier, a woman and her five children, all under the age of 13, were killed when an air raid destroyed their house in Jabaliya, north of Gaza City, according to medics.
Hatem Shurrab, a Gaza resident living near Tar al-Hawa in Gaza City, which has experienced some of the heaviest fighting, told Al Jazeera that regular explosions could still be heard.
"I have my sister's family who came to our home to shelter. It's very difficult to describe how we feel. It's very scary. The next target is not known. Who will be killed next, we don't know.
"I can hear explosions going around and a couple of hundreds of metres away a home was burnt close to the explosions.
"What is really painful for me is that I see every day people who are being displaced. Mass internal displacement. Women running in the street trying to find a place."
Meanwhile, a funeral was held for Said Siam, the interior minister in Hamas's government, who was assassinated on Thursday along with one of his sons and a brother in an air raid in Jabaliya refugee camp.