"There is a possibility that the militants are fighting to protect al Qaeda number 2. This is a strong possibility," said a government official who did not wish to be identified.
The official was speaking after President Pervez Musharraf told CNN that his forces believed they had a "high-value target" surrounded because of the fierce resistance they had encountered.
Information Minister Sheikh Rashid told AFP intense fighting was going on in South Waziristan's Azam Warsak area between troops and militants, but said, "we cannot confirm the presence of any named al Qaeda figure.
"The possibility of an important figure being surrounded cannot be ruled out," he said
Another official said: "fierce fighting is going on between Pakistani forces and militants entrenched on hilltops and fortress like houses in the area for the past more than 13 hours."
A US official said in Washington that Pakistani authorities believed they had surrounded a senior member of al Qaeda in the tribal areas near Afghanistan.
The official, who spoke on condition of anonymity, would not confirm reports that Zawahiri, the right hand man of al Qaeda leader Osama bin Laden, had been surrounded on the Pakistan-Afghanistan border.
"The Pakistanis believe they have a high-value target, a senior al Qaeda member surrounded. But I can't confirm who that is," the official said. "We can't confirm what they are saying. It's what they believe."
Musharraf told CNN: "We feel that there may be a high-value target. I can't say who."
Asked whether there was heavy fighting, Musharraf said: "Yes, the resistance that is being offered by the people there, we feel that there may be a high-value target. I can't say who." He went on to say: "They are giving fierce resistance so we are pretty sure there is a high-value target there."
A senior Pakistani intelligence official said, "we do not have any specific intelligence about the presence of Zawahiri."
The Pakistan government plans an air-strike on Friday at a group they believe to be cornered al Qaeda fighters including No 2 Ayman al-Zawahri, CNN said, citing Pakistani government sources.
"Sometime after light fall it sounds like they will go in with helicopter gunships and they may go in with fixed wing. ... The plan is to go in by air tomorrow, or at least first light," CNN correspondent Aaron Brown said, speaking from Pakistan.