Omar Suleiman, the head of intelligence recently tapped as President Hosni Mubarak's vice president, was involved in the discussions, The New York Times said. Egyptian and U.S. officials said Suleiman would oversee the transition to a more democratic regime.
While some members of the opposition said they fear a military coalition would lead to a repeat of Mubarak's 30-year rule, protesters cheered Field Marshal Mohamed Tantawi when he visited Tahrir Square, the Times said. Tantawi, the defense minister, has close ties to Suleiman.
Tens of thousands of demonstrators filled the square after Friday prayers, carrying signs in Arabic and English telling the 82-year-old Mubarak to relinquish office.
"Leave! Leave!" urged protesters, who dubbed the 11th day of protests the "day of departure."
"We are not leaving! You are leaving!" the Los Angeles Times said they yelled to drown out a helicopter that was hovering overhead.
Largely peaceful demonstrations were reported in all of Egypt's administrative districts, al-Masry al-Youm reported, putting the number of protesters in the hundreds of thousands.
Health Minister Ahmed Fareed said 28 people were injured during Friday's protests and two remained hospitalized with broken bones. Since Wednesday, 11 people have been killed and 1,134 injured, he said, with 111 still hospitalized.
The United Nations indicated upwards of 300 have died and 4,000 have been hurt since the unrest began Jan. 25.
In an interview with ABC News Thursday, Mubarak said he was fed up with being president and would resign but fears the country would descend into chaos if he left immediately.
Opposition leader Mohamed ElBaradei dismissed the assessment, telling the BBC Mubarak's attitude is "symptomatic of a dictatorship. He thinks if he leaves power the whole country will fall apart."
Prime Minister Ahmed Shafiq said the government has met 80 percent of the protesters' demands and Mubarak's decision not to seek re-election in the fall in effect meets their demand he step down. Al-Arabiya reported Mubarak was planning to hand over power to Suleiman.
A group of 18 intellectuals -- the "Committee of Wise Men" -- said they have been in communication with Suleiman and Shafiq, who said in a statement on the al-Hurra satellite channel Mubarak should leave in a dignified manner.
"The truth, to be very clear, is that if it were possible to hold a general vote regarding demands to have Mubarak leave now, 90 or 95 percent of Egyptians would say that it is all a matter of five months," Shafiq said, adding everything is negotiable.
A spokesman for Al-Azhar University told CNN Friday he resigned from his position and joined the anti-government protesters. Al-Masry al-Youm reported three members of Egypt's upper parliamentary chamber resigned to join the protest.
Leaders of the Muslim Brotherhood said the movement, banned in Egypt, doesn't plan to nominate a candidate for the presidential elections, spokesman Mohammed al-Beltagi told al-Jazeera satellite television Friday.
"We have said clearly that we have no ambitions to run for the presidency or posts in a coalition government," he said.