Ben-Eliezer added that in his experience, Prime Minister Ehud Olmert would not reject any offer outright.
Meanwhile, security sources quoted by Army Radio said Israel would not be able to ignore Hamas's offer of a ceasefire if it proved able to halt Kassam attacks. The sources added that no negotiations were taking place at the moment.
The Prime Minister's Office denied late Thursday night that Israel was considering a Hamas ceasefire proposal, Israel radio reported.
Earlier, defense officials, speaking on condition of anonymity, had said that Israel was considering a ceasefire, whereby Hamas would stop the rocket fire from Gaza in exchange for a halt in IDF operations in the Strip. They said Hamas gave assurances it could impose the truce on the militant groups that are firing the rockets - Islamic Jihad and the Popular Resistance Committees.
There was no immediate comment from the Egyptian government.
Meanwhile, Hamas admitted that it had fired three Kassam rockets at an IDF post on the Gaza border.
It marks the first time in five months the group has fired a rocket, although Israel estimates that it has assisted other groups in their attacks.
Also Thursday, the Palestinian Pal Press agency quoted "informed Arab sources" as saying that Hamas's Damascus-based leader Khaled Mashaal pushed Hamas Prime Minister Ismail Haniyeh to call a Channel 2 reporter during which the Hamas leader reportedly offered Israel a "hudna."
According to the report, Mashaal instructed Haniyeh to call the reporter and convey to the Israeli government the message that Hamas was interested in negotiating a ceasefire. Mashaal also reportedly demanded that Haniyeh's forces maintain quiet along the border with Israel.
Israel and Hamas have engaged in dialogue in the past "via indirect tracks," according to the sources quoted by the report. For instance, they said, the two sides had negotiated the departure of pilgrims from amongst the ranks of Hamas to the haj in Saudi Arabia.
"Israel allowed the people through, but rejected a number of other names, including senior Islamic Jihad [activist] al-Hindi, and Majed Harazin, who was assassinated in Gaza two days ago," the sources said.
Responding to Haniyeh's offer Wednesday, Transportation Minister Shaul Mofaz said in media interviews that Israel had already engaged in contacts with Hamas through mediators on issues such as the efforts to bring home kidnapped soldier Gilad Schalit, so there was no reason not to do the same to end the rocket attacks.
Gil Hoffman and Herb Keinon contributed to this report.