The officials say the plan, approved by the country's security cabinet, also includes the displacement of hundreds of thousands of Palestinians to southern Gaza.
The officials spoke on condition of anonymity because they were discussing military plans.
The plan, which one official said would be gradual, would mark a significant escalation in the fighting in Gaza, which resumed in mid-March after Israel and Hamas failed to agree on an extension to an eight-week truce.
On Sunday, Israel's military chief of staff, Lieutenant General Eyal Zamir, said the army was calling up tens of thousands of reserve soldiers and said Israel would "operate in additional areas" in Gaza and continue to strike militant infrastructure.
Israel already controls roughly half of Gaza's territory, including a buffer zone along the border with Israel as well as three corridors that run east-west along the strip.
These have squeezed war-weary Palestinians into ever shrinking wedges of land in the devastated territory.
For weeks, Israel has been trying to ratchet up pressure on the militant Hamas group and prompt it to show more flexibility in negotiations.
In early March, Israel halted the entry of aid into Gaza — a ban that is ongoing and which has plunged the territory of 2.3 million people into what is believed to be the worst humanitarian crisis of the war.
Hunger has been widespread, and shortages have set off looting.
On March 18, Israeli resumed strikes in the territory, killing more than 2600 people in the weeks since, many of them women and children, according to local health officials.
The previous ceasefire was meant to lead the sides to negotiate an end to the war, but that end goal has been a repeated sticking point in talks between Israel and Hamas.
Israel says it won't agree to end the war until Hamas is defeated. Hamas meanwhile has demanded an agreement that winds down the war.
The war in Gaza began when Hamas-led militants attacked southern Israel, killing 1200 people and taking about 250 hostages. Israel says 59 captives remain in Gaza, although about 35 are believed to be dead.
Israel's offensive has killed more than 52,000 people in Gaza, many of them women and children, according to Palestinian health officials, who do not distinguish between combatants and civilians in their count.
The fighting has displaced more than 90 per cent of Gaza's population, often multiple times, and turned Gaza into an uninhabitable moonscape.
