Pasha may quit as the Pakistan government "looks for a fall guy for the bin Laden debacle", unnamed senior officials were quoted as saying by The Daily Beast, a news website affiliated to Newsweek magazine.
The senior officials said "they recognise that an important head has to roll and soon" to allay domestic and international anger over bin Laden''s presence in Abbottabad, located close to the federal capital of Islamabad.
The officials said the "most likely candidate to be the fall guy is Lt Gen Ahmed Shuja Pasha".
They said it was "nearly a done deal". Pakistani analysts with close connections to the military agreed.
"It would make a lot of sense...It's in his (Pasha's) personal and the national interest to take the heat off," said Lt Gen (retired) Talat Masood, one of Pakistan's leading defence analysts.
An official statement issued yesterday after a meeting of Corps Commanders chaired by army chief Gen Ashfaq Parvez Kayani said the military admitted its "own shortcomings in developing intelligence on the presence of Osama bin Laden in Pakistan".
It added that "an investigation has been ordered into the circumstances that led to this situation".
The Daily Beast reported that Pakistanis were furious that the ISI and the powerful military, which control national security policy, "could have been so incompetent not to know that the al Qaeda leader was comfortably holed up in Abbottabadd", only 80 km north of Islamabad.
"Never before have the military and the ISI come under such criticism," said Masood.
People are angry that the military, which gets the lion's share of the budget, could be totally unaware that US helicopters had violated Pakistani airspace during the raid that killed bin Laden on Monday.
Pakistani officials, both from the civilian government and the military, have said the US did not inform them about the raid.
"People are outraged...They see this as the fault of the military in which they have invested so much trust," Masood was quoted as saying.
However, a senior ISI officer told The Daily Beast he could not confirm the report and he had no knowledge of Pasha being "pressured into resigning".
The officer said, "It's far from routine for someone to resign over failures. But someone has to resign."
A former ISI officer was more blunt, the website reported.
"It was a great failure of, and an embarrassment to Pakistani intelligence. The pressure is mounting for Pasha to resign," he said.
Pasha's resignation could be the first step in a process of rebuilding that badly damaged confidence, Masood and senior Pakistani officials said.
"It could ease a lot of pressure," Masood said.
It would also help rehabilitate the army's and the ISI's badly tarnished image.
The senior Pakistani officials said Pasha was never keen on the ISI job in the first place as he had no background in intelligence and was an infantry and armour officer in previous commands.
He was, however, very close to Kayani, who insisted he take the job when he was nominated as army chief in 2008.
Pasha had served under Kayani's command as an infantry officer and had served as head of military operations just as Kayani had.
Kayani also headed the ISI during 2004-07 until former military ruler Pervez Musharraf appointed him army chief.
Pasha has been given two extensions as the ISI chief, the latest earlier this year.