Prime Minister Blair could become a part-time peace envoy to the Middle East when he quits Downing Street next week after being urged to take on the role by President Bush.

As job offers for the prime minister pile up, White House officials disclosed that Mr. Bush and Secretary of State Rice discussed the idea with Mr. Blair recently.

They want him to become special envoy for the so-called “quartet” of powers — the United Nations, America, the European Union, and Russia — which is heading the push to find a solution to the Israeli-Palestinian Arab conflict.

Downing Street refused to discuss Mr. Blair’s future plans last night but did not rule out the possibility that he could take on such a role. Mr. Blair will step down as prime minister next Wednesday — June 27 — after more than a decade in power. He has said he has “no idea” what he will do after he leaves office.

However, Mr. Blair is known to be interested in taking a variety of roles on the world stage, particularly ones involving efforts to broker peace in the Middle East, help the fight against poverty in Africa, and combat global warming.

Allies of the prime minister say he is not interested in taking on a single formal post. Instead, he wants a more mixed and varied portfolio and the freedom, as far as possible, to determine his own timetable. Mr. Blair wants to remain a statesman in world affairs rather than retire into the moneyspinning world of business and speech-making.

The position of envoy to the “quartet” has been vacant since James Wolfensohn, the former president of the World Bank, stepped down in April 2006. A spokesman for Prime Minister Olmert of Israel said yesterday that Mr. Blair could serve as a “mentor” to the emergency Palestinian Authority government.