Yet conversations with U.S. and Afghan officials and members of the former Taliban government make clear that, even today, no one is certain who can speak for Omar. Nor do they know what he wants. (Despite last week's rumors of his death, he is believed to still be alive, and hiding in Pakistan.)
So any talk of talks to hasten the end of the conflict and speed the U.S. troop exit is still very premature.
"We encourage the United States to hold these meetings to find out if there is something serious," I was told by President Hamid Karzai's national security adviser, Rangin Dadfar Spanta, at the heavily guarded presidential palace.
"We have had serious contacts with Taliban," he went on, "but the question is, are they in charge, are they representative of the Quetta shura? They have to prove it. We don't want a second episode like the grocer." Spanta was referring to a Taliban mullah who was brought to meet Karzai last year, after being paid a hefty sum of money: He turned out to be an impostor, who was actually a shopkeeper.
Spanta added that "the United States itself is not sure" about the bona fides of Agha, a man in his mid-30s with a thin beard, who used to head Omar's international relations committee. "Is he really Tayyeb Agha? Is he still the representative of Mullah Omar? We have to prove it."
And that is only the beginning of the hurdles that confront an effort to get the Taliban to talks.
Mohamed Masoom Stanekzai, the professorial secretary of the Afghan High Peace Council, says it is essential that "the Taliban should have an office," with a representative who could speak for its leaders. In other words, the Taliban should set up a political front group like a Sinn Fein.
Stanekzai says such an office should be located outside of Pakistan, where the Quetta shura is based, so Taliban reps could operate free from control by Pakistan's ISI intelligence agency. Many Afghans are convinced the ISI would block any talks that it could not direct.
But all this begs the question of whether the Taliban is really interested in talks or has clear negotiating positions, beyond its demand that foreign troops leave Afghanistan.
Stanekzai, whose council has had contacts with the Taliban, says most of Omar's inner circle "are on the side of the peace process." He says they are afraid to discuss this publicly, however, lest they be branded as traitors by their rank and file.
However, other Afghans familiar with the Taliban say its leadership thinks it is winning the Afghan war, and has little interest in negotiations.
"Mullah Omar wants an Islamic emirate and says, 'We will never share power with anybody,' " says Waheed Mozhdah, a writer who worked in the Taliban government for five years. "They think they've defeated the United States, like they defeated the Soviet Union, and this is the start of another era."
Mozhdah has argued with Taliban friends that Afghanistan has gained little from defeating the Soviets, and needs economic development more than another such victory. Whether the Taliban can be persuaded by such arguments is unknown.
U.S. and Afghan officials have laid down clear red lines: For any talks to succeed, the Taliban must break with al-Qaeda, accept the Afghan constitution, and play by democratic rules.
Would the Karzai government offer a power-sharing deal that guaranteed the Taliban control of certain provinces or ministries? "Absolutely not," said Spanta. The Taliban could acquire major government posts, he said, but only as part of a democratic process. Many doubt Mullah Omar would ever agree.
So here we have it. We don't know who speaks for the Taliban or what they want, or whether Mullah Omar could deliver a fragmented organization, even if he wanted to do so. We don't know if a way can be found to bring Pakistan productively into the negotiating process.
Moreover, a majority of the Afghan population opposes any deal that might foster a Taliban regime redux. The Taliban are ethnic Pashtuns, but an opposition movement of non-Pashtuns is mobilizing. Any pact that heedlessly opened the way for a Taliban comeback could provoke civil war.
And yet, despite all of the above, there are good reasons to keep exploring talks, so long as it is done without illusions. Perhaps the Quetta shura is tiring. Perhaps the movement is splitting. We need to find out.
So proceeding with caution is warranted, with no illusions that talks are imminent or a panacea. As a first step some detective work is urgently needed: Find out if Tayyeb Agha is for real.
E-mail Trudy Rubin