For years the project was a distant prospect because of the Israeli-Palestinian conflict - peace talks between the two sides broke down in 2014 and never resumed, amid mutual suspicion and outbreaks of violence.
But Israeli, Palestinian, Qatari and European interests have converged in recent weeks with the aim of getting gas flowing to Gaza in 2023, say the officials.
The plan would see natural gas from the deepwater Leviathan field operated by Chevron in the eastern Mediterranean flow through an existing pipeline into Israel, and from there into Gaza through a proposed new extension.
Under the arrangement, which has yet to be finalized, the Israeli side of the planned pipeline would be funded by Qatar and the section in Gaza paid for by the European Union, the officials told Reuters.
If successful, the pipeline project would for the first time in years provide a steady energy source to the Gaza Strip, ending rolling blackouts that have helped cripple the economy of the blockaded Palestinian enclave.
"We are talking about Gaza having 24 hours of electricity, providing a basis for major economic growth and a contributor to peace and stability," said Ariel Ezrahi, director of energy for the Office of the Quartet, a group promoting peace efforts between the Palestinians and Israelis which reports to the United States, United Nations, European Union and Russia.
"Recent events have constituted a real breakthrough," said Ezrahi, who chairs the Gas for Gaza task force that has been funded by the Dutch government since 2015.
LEVIATHAN
The Quartet office sees the Palestinians initially buying about 0.2 billion cubic meters (BCM) of gas a year, perhaps rising to 1 BCM as the plant expands and other consumers join.
The European Union last week committed an initial 5 million euros to fund the Gaza portion of the pipeline, which will run about 4km and cost around 20 million euros.
Qatari envoy to the Gaza Strip Mohammed Al-Emadi last week told Gaza-based news agency SAWA that his country would fund the Israeli segment of the pipeline, which officials say will stretch some 45km and cost around 70 million euros.
Palestinian and Israeli officials told Reuters that Qatar is ready to pay for the pipeline in Israel. Emadi's office and Qatar's government press office did not respond to Reuters queries.
Israel's Leviathan field is already exporting gas to neighbouring Jordan and Egypt.
Asked about the Gaza pipeline, Chevron said it looked "forward to supporting Israel's strategy to develop its energy resources for the benefit of the country and the region" but that it did not comment "on matters of a commercial nature".
Its main Israeli partner in Leviathan, Delek Drilling , declined to comment.
SEALED OFF
Gaza, home to two million Palestinians, is a 360 sq. km coastal enclave that lies between Egypt's Sinai peninsula and Tel Aviv.
It has no access to the outside world except through Israel, which controls 90% of its land and sea boundaries, and Egypt, which has a narrow land border to the south.
Both countries have for years maintained a tight blockade, citing security concerns about the Islamist militant group Hamas, which seized control of Gaza in 2007.
Today, Gaza's sole power station produces electricity for around 12 hours a day on diesel, a more expensive and polluting fuel.
The pipeline will enable the power station to double, perhaps quadruple, generation capacity. The Quartet office estimates it will add more than $1 billion to the Palestinian gross domestic product.
POLITICS AND POWER
While a cheaper and more reliable source of power might ease the economic plight of Gazans - thereby contributing to stability in the region - few expect it to be a panacea.
Indeed the power station at the end of the proposed pipeline has already proved vulnerable to politics.
In 2006 it was bombed by Israel after Hamas militants from Gaza captured an Israeli soldier in a cross-border raid.
And over the past decade a bitter feud between Hamas and its main domestic rival, President Mahmoud Abbas, has seen the two sides accuse each other of worsening the power crisis.
Abbas's western-backed Palestinian Authority will be handling the final talks with the Israeli gas company, Palestinian officials said.
Palestine Electric Company (PEC) vice chairman Walid Salman said he hoped agreement could be reached in weeks - allowing electricity costs to drop 60% and generation to double to a maximum 140 megawatts.
He said they have been speaking to Delek about a 5-year gas deal.
In Israel, Energy Minister Yuval Steinitz said the project was being done "in full coordination with us."
That includes the defense establishment and state-owned Israel National Gas Lines, whose CEO said plans for a 24-inch pipeline that can carry "significant amounts of gas" are ready.
They are waiting for a final deal, perhaps in the coming weeks, to begin construction.