The Times of Israel reported the development early on Monday, citing senior officials.
The plan is expected to be implemented only after US President Donald Trump's visit to the region next week, the Times said.
In the meantime, efforts will focus on reaching a ceasefire and hostage deal with Palestinian militant organisation Hamas, according to the report.
The security cabinet also approved a plan to renew aid deliveries into Gaza, while overhauling the distribution system to reduce the risk of Hamas diverting supplies for its operatives.
For over two months, Israel has not allowed aid deliveries into the sealed-off area, home to around two million Palestinians, prompting allegations it is using starvation as a weapon.
The United Nations rejected the proposal to deliver aid into Gaza under military-controlled conditions in a statement on Sunday, citing serious humanitarian concerns.
The UN humanitarian team in Gaza said Israel's plan would violate core humanitarian principles and appeared "designed to reinforce control over life-sustaining items as a pressure tactic - as part of a military strategy".
The proposed delivery mechanism would require UN approval to distribute supplies through Israeli checkpoints under conditions set by the Israeli military.
The UN team warned the proposed strategy would force civilians into militarised zones to collect rations, placing both them and aid workers at risk.
Vulnerable people with limited mobility may not be reached and the plan would likely contribute to further forced displacement.
The UN said it could only support schemes that uphold the humanitarian principles of humanity, impartiality, independence and neutrality.
Israel has blocked all humanitarian aid into Gaza since early March, halting deliveries of food, clean water and medicine.
UN officials warn that civilians are going hungry and hospitals are unable to treat the sick and wounded.
Israel says the blockade aims to pressure Palestinian militant group Hamas to release remaining hostages taken during the October 7, 2023, attack.
The UN has repeatedly called for the unconditional release of all hostages.
The UN also reiterated that international law prohibits collective punishment and obliges occupying powers to ensure the welfare of civilians.
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