The Quartet of Middle East mediators is considering naming Tony Blair for a top peacemaking post, diplomats say.
Mr Blair steps down on Wednesday as UK prime minister and officials from the EU, Russia, the UN and US are working to define a possible new role for him.
It is the Quartet's first meeting since Hamas militants took control of security from pro-Fatah rivals in Gaza.
The US has signaled its desire for a role for Mr Blair, but many Arabs see him as too pro-American and Israeli.
The outgoing prime minister signaled his interest in taking the job, as he spoke to reporters following a meeting with California governor Arnold Schwarzenegger at Downing Street.
"I think that anybody who cares about greater peace and stability in the world knows that a lasting and enduring resolution of the Israeli-Palestinian issue is essential," Mr Blair said.
"And I will do whatever I can to help such a resolution come about."
The Middle East situation has become more critical in the last two weeks, as a Palestinian unity deal collapsed between the Islamist Hamas and secular Fatah.
Fighting erupted on the streets of Gaza, with Hamas gunmen routing the pro-Fatah security forces.
Palestinian Authority President Mahmoud Abbas, of Fatah, responded by dissolving the Hamas-led cabinet, bringing about the division of Gaza and the West Bank as separate fiefdoms.
Criticism
Mr Blair is a controversial figure in the Middle East, primarily because of the war in Iraq.
He was also much criticized in the region for refusing to condemn Israel's bombardment of Lebanon in 2006 and to call for an early ceasefire.
BBC Jerusalem correspondent Tim Franks says Israeli officials enthuse about Mr Blair's status and experience. Palestinians are far more skeptical.
The Russians are said to be cool about his possible appointment, but are not expected to block it.
A spokesman for the Islamist Hamas group said that "the experience of our people with Blair was bad" and his appointment "may even make things worse".
The meeting at the US consulate in Jerusalem was closed to the media and the British Embassy in Tel Aviv would not confirm reports that Mr Blair's role was under discussion.
Reports in the British media said he would not act as a mediator to end the Israeli occupation of the West Bank and Gaza, but might be responsible for working with the Palestinians on security, economy and governance.
Boost
The Quartet meeting follows a summit between the leaders of Egypt, Jordan, Israel and the Palestinians in Sharm el-Sheikh aimed at boosting Mr Abbas and Fatah movement after he named an emergency cabinet of his supporters.