Citing a senior military official, the newspaper said that the plan, which will require government approval, will have an initial price-tag of $40-70 million and will be presented at the end of the month.
The plan covers an area of sea about 1.5 times the size of Israel, the newspaper said, extending far out into the Mediterranean.
Israel says the gas fields all lay in its waters, but neighbouring Lebanon which remains technically at a state of war with the Jewish state, says one of them lies partly on its side of their undemarcated maritime border.
The Tamar field, which Lebanon contests, holds reserves of natural gas estimated at 8.4 trillion cubic feet (238 billion cubic metres), while the Leviathan field is thought to hold twice that, around 16 trillion cubic feet (450 billion cubic metres).
The fields could be large enough to cover around 70 percent of Israel's electricity usage, and also allow the Jewish state to become an energy exporter.
A military spokesman questioned by AFP declined to confirm or deny a defence plan for the gas fields.