Postcards of Bin Laden are on sale in Pakistan
The reports come as anti-Taleban and US forces have stepped up the fight to take the Tora Bora caves and the White Mountains close to the Pakistan border.
But speaking on Thursday, US Defence Secretary Donald Rumsfeld said Osama Bin Laden was still believed to be in Afghanistan.
"We think he's in Afghanistan, we are chasing him, he is hiding, he does not want us to know where he is, we are asking everyone we can to help," Mr Rumsfeld said.
Witness
"Bin Laden travelled out of Tora Bora twice in this Ramadan holy month," Abu Jaffar told the Daily Telegraph.
"He left to meet the Taleban leader Mullah Omar about three weeks ago and stayed with him near Kandahar.
"He left again just over a week ago and was headed to Pakistan, where he was helped across the border by Pashtun tribesmen."
According to Mr Jaffar, who remained in Tora Bora until his foot was blown off by a cluster bomb, Bin Laden had sent his 19-year-old son Salah Uddin to fight with them.
"Salah Uddin told me to leave and he gave me money because I will likely need another operation on my leg," Mr Jaffar said.
Reports from the region around Tora Bora suggest that Bin Laden and the remaining al-Qaeda fighters may have moved higher up the White Mountains to try to cross into Pakistan.
Once inside Pakistan, the argument goes, they would be received by Pashtun tribesmen sympathetic to their cause, and be spirited away from the border area.
The rugged frontier is difficult to police, and is an autonomous zone within Pakistan where security matters are usually left to the local tribes.
Media reports
In the absence of any definite news of Bin Laden's whereabouts, media sources have carried a variety of unconfirmed reports.
A correspondent for the al-Jazeera TV station said he had been told by people close to the al-Qaeda organisation that Bin Laden had left the Tora Bora caves "three or four days after the area was besieged".
The BBC regional analyst says he could be on the move in the area with a small group of hardened fighters who are unquestioningly loyal to him.
French TV reported the possibility that he had left Afghanistan by helicopter, for either Yemen or Africa.
This was based on a French helicopter pilot alleging he knew of a colleague being offered $5m to fly Bin Laden out of Afghanistan.
Another report from the Pakistani newspaper al-Akhbar on Wednesday said Bin Laden and the Taleban leader Mullah Mohammad Omar had been shot with their own consent in Kandahar the day the city fell to anti-Taleban forces.
This unconfirmed story was brought to Karachi by Afghan families fleeing to Pakistan, the newspaper said.
The BBC regional analyst also says that Bin Laden probably has no intention of being taken alive and put on trial.
"He seems ready to die, in the firm belief that after him will come other Bin Ladens to continue the struggle," he says.
Interview
The last confirmed contact with Bin Laden, more than a month ago, put him somewhere north of Jalalabad, where he is thought to have had several training camps.
Journalist Hamid Mir, editor of the Dawn newspaper in Pakistan, was wrapped in a blanket and driven for five hours from Kabul before interviewing Bin Laden.
Mr Mir recalled colder temperatures and the sound of anti-aircraft fire, which could mean he was driven north from the capital as it came under attack from US planes and anti-Taleban forces.
But Mr Mir said that, by holding the interview in the north, Bin Laden may have trying to draw attention away from his bases elsewhere in the country.