Palestinians wait hoping to be given the permission to cross into Egypt at the Rafah crossing between Egypt and the southern Gaza Strip in late August as a cease-fire ended two months of bloody fighting. SAID KHATIB/AFP/Getty Images

JERUSALEM – Israel’s Army Radio caused a stir here Monday when it reported that Egyptian President Abdel Fattah al-Sissi had proposed ceding parts of his country's territory in the Sinai Peninsula to create an autonomous, demilitarized Palestinian state. The plan, according to the radio report, was rejected last month by Palestinian Authority President Mahmoud Abbas.

The report was brief and it was attributed to anonymous sources. It was also flatly denied by all parties involved, with Egyptian state media quoting Sissi as saying “no one can do that” and Palestinian presidential spokesman Nabil Abu Rudeinah releasing a statement saying no such proposal had ever been discussed.

Nevertheless, after a summer of bloody warfare in the Gaza Strip, the concept of an expanded Palestinian state in the sand dunes of the Sinai desert as a possible solution to the Israeli-Palestinian conflict was immediately thrown into the spotlight -- and heartily embraced by some Israeli politicians.

“What a wonderful proposal by the Egyptian president to give the Palestinians land five times the size of Gaza to create their state,” Israel’s Transportation Minister Yisrael Katz wrote in a Facebook post.

Israel’s Minister of Science and Technology, Yaakov Peri, told Army Radio that it was certainly a “creative proposal,” and a worthwhile one for Israel to examine in more detail, despite Abbas’s purported rejection.

According to the radio report, Egypt would give up nearly 1,000 square miles of its territory adjacent to Gaza and, in return, Abbas would drop on his demands to form a Palestinian state within the 1967 lines that once divided Israel and Jordan.

The Palestinians, the report said, would continue holding onto areas in the West Bank that are currently under the control of the Palestinian Authority, but the expanded Gaza strip would form the bulk of Palestinian lands.

The idea of of expanding the coastal enclave into Egypt has been broached in the past by Israeli academics and leaders -- who, in the view of many Palestinians, very much want to foist Gaza onto Egypt, in part to further split the population of Gaza from that of the West Bank.

In 2008, the former head of Israel's National Security Council, Giora Eiland, suggested Egypt transfer some of its land to help form a Palestinian state and in return Israel would ease its restrictions on Egypt’s military presence in the Sinai. Eiland's plan was to add a square at the northwestern tip of the Sinai Peninsula onto the 140-square-mile Gaza -- a space, according to Eiland, that is far too small to successfully support its more than 1 million residents. The plan was rejected at that time by Egypt.

Abbas met with the Egyptian president in Cairo last week, and throughout the summer's war in Gaza, he consistently supported Sissi's ceasefire plan. But tensions remain high between Egypt and Hamas, the militant Islamist group that controls Gaza and is an offshoot of Egypt's Muslim Brotherhood, which Sissi's military-backed government has declared a terrorist group. Egypt has also been struggling to regain control of the vast Sinai desert, where unrest and Islamist extremism have simmered since the 2011 revolution in Egypt.

The Palestinian Maan News Agency reported Monday that al-Tayyib Abd al-Rahim, the secretary-general of Abbas's office, as saying that the Palestinian leadership would not accept any alternative to a Palestinian state on 1967 lines with East Jerusalem as its capital.”

Despite the interest -- and, perhaps, wishful thinking -- in Israel, Ruth Wasserman Lande, a former diplomat at the Israeli embassy in Cairo, insisted the plan “had nothing to do with Israel.”