"Not everyone is on board with that though. One of the main security figures in Israel Yuval Diskin [the head of the Israeli security agency], yesterday said that he opposes the lifting of the blockade.
"But in essence, what the Israeli cabinet is considering is a shift in policy."
The proposal to ease the blockade was first announced earlier this week by Tony Blair, the envoy from the so-called international peace Quartet, comprised of the US, the UN, the European Union and Russia.
It would allow the UN to ship much-needed construction materials into Gaza for its own use.
"It will allow us to keep weapons and weapon materials out of Gaza, but on the other hand to help the Palestinian population there," Blair told the Israeli newspaper Haaretz.
"The policy in Gaza should be to isolate the extremists but to help the people."
Any new policy will reportedly only apply to the land border crossings between Israel and Gaza. The Israeli navy will maintain its blockade of Gaza.
The UN has called for Israel to go further and completely end the blockade.
"The flotilla crisis is the latest symptom of a failed policy," Robert Serry, the UN Middle East envoy, said in a briefing at the Security Council on Tuesday. "The closure and blockade of Gaza needs to come to an end."
The International Committee of the Red Cross said on Monday that the blockade is illegal, and called on the Israeli government to lift it.
Separately, the Israeli government has agreed to allow the UN to deliver thousands of tonnes of aid seized from a Gaza-bound aid flotilla last month.
The UN will supervise delivery of the cargo, which includes construction supplies
Until Tuesday, Hamas had refused to accept the aid, citing Israel's limitations on how much of it would be allowed into Gaza.
But the UN said it will deliver the entire cargo, which includes food, medicine and clothing.
"[We have] obtained the consent of the cargo owners of the three Turkish-registered vessels to take possession of, and responsibility for, the entire cargo, and to ensure its timely distribution in Gaza for humanitarian purposes," Serry said.
Israel took control of the cargo after its deadly May 31 navy raid on the flotilla.
Nine Turkish activists were killed in the attack.
Meanwhile, the committee established by the Israeli government to investigate the flotilla attack is expected to hold its first meeting on Wednesday.
The meeting will probably focus on formalities: deciding where the committee will work, and setting a budget and a schedule for testimonies and meetings.
Jacob Turkel, the committee chair, who is a retired supreme court judge, did not announce a time or location for the meeting.
Also on Wednesday, George Mitchell, the US Middle East envoy, returned to the region for meetings with Israeli and Palestinian officials.
He is also preparing for a meeting later this month between Barack Obama, the US president, and Binyamin Netanyahu, the Israeli prime minister.