As Prime Minister Blair ponders whether he should assume the title of Israeli-Arab peace-processor in chief, the first question that should pop into his mind is the one most overlooked in the excitement that has accompanied the mere prospect of his entering the Middle East fray: Is there any peace to process?

Mr. Blair has already been mentioned as a candidate for a U.N. secretary-generalship, World Bank presidency, or European Union chiefdom, to name but a few. But in the last two days, Washington aggressively floated his candidacy to head the Middle East Quartet, making it the most promising of the major international positions potentially occupying his time after he leaves no. 10 Downing Street next Wednesday.

Secretary of State Rice raised the Blair nomination with Secretary-General Ban in a telephone conversation yesterday, and Mr. Ban is said to favor the idea. Although Russia, one of the members of the Quartet — along with America, the European Union, and the United Nations — is unenthusiastic, internationalists the world over should be ecstatic at the prospect of a figure of Mr. Blair’s stature leading the way.

Not everyone at Turtle Bay is happy, though. Only days ago, the building was abuzz about the bravado displayed in a now-famous “confidential” memo by a former Middle East envoy, Alvaro de Soto. In his witty whine, the Peruvian envoy advocated that the United Nations quit the Quartet, arguing that the world body could strike peacemaking gold on its own — unburdened by the yoke of a discredited American diplomacy.

The reality is the reverse. Thank to the one-sided policies of Mr. de Soto’s generation of international diplomats, the United Nations was for decades taken out of the calculations of Israeli policymakers. While the Quartet is marginal at best, it is at least recognized as legitimate in Jerusalem, giving some credence to the input of all four members, including the United Nations, which otherwise would have no say whatsoever.

While Mr. de Soto blames past U.N. sins, like the “Zionism is racism” resolution, for its marginalization in the eyes of Israelis, the entire U.N. system remains more interested in condemning Israel than in advancing the welfare of its Palestinian Arab clients.

Yesterday, the point man for the “occupied Palestinian territories” at the Office for Coordination of Human Affairs, David Shearer, briefed U.N. reporters about the current humanitarian situation in Gaza, which two years after Israel’s disengagement remains “occupied” in U.N. lingo.

The briefing concentrated on Israeli sins in the West Bank and Gaza — settlements, roadblocks, checkpoints, and withholding building permits inside nature preserves (a strange complaint from the normally green United Nations). Mr. Shearer, who could have delivered the same briefing two months ago, stopped at the Israeli border. Humanitarian suffering created in Gaza by last week’s Hamas-Fatah civil war remained unaddressed.

Lacking the hubris of U.N. diplomats, other Quartet partners know that membership has its privileges. “Sometimes, we have tactical differences,” Russia’s ambassador to the United Nations, Vitaly Churkin, told me recently. Like Mr. de Soto, Moscow is arguing for the inclusion of Hamas in peace talks even as the other three members call to marginalize it. Right or wrong, this argument by Moscow would be lost outside the group, and therefore, as Mr. Churkin said, “We continue to believe that the Quartet is a very important international instrument.”

And with Mr. Blair at the helm, a renewed edge is promised for this blunt diplomatic instrument. While most of Mr. Ban’s closest aides know this, others fear that, as one U.N. official described it, the charismatic Mr. Blair would “like Clinton, suck all the air out of the room,” relegating other Quartet members to a rubber-stamp status.

Ever since Al-Jazeera first speculated about Mr. Blair’s new prospect, chattering classes around the world ran with it, with one glaring exception: the normally edgy Israeli press so far has all but ignored the story.

Perhaps this is because too many has-been world-class politicians, from Count Bernadotte to George Mitchell, have tried their hand at processing peace between Israel and the Arabs. Perhaps Israelis don’t know which warring Palestinian Arab faction they should deal with — the one explicitly calling for the Jewish state’s destruction, or the one implicitly doing so.

Israelis are increasingly convinced that the problem is not in finding a new magic formula to be sold by a new magic man. “Jews don’t have the diplomatic and moral option of rejecting any peace initiative,” a politically centrist veteran columnist, Dan Margalit, wrote recently in Ma’ariv. “But there is no one to talk to.”

Noting that he had always supported dovish Israeli policies — from Oslo to the Gaza withdrawal — recent events convinced Mr. Margalit that no compromise is currently feasible. This “does not mean we will never achieve peace,” he wrote. “But until the Palestinians reach the point that they are interested in it,” Israel must battle terrorism “without constantly whining about it.”

This is also not such bad advice for Western shapers of policy on Lebanon, Iraq, and the rest of the Middle East.