A former senior intelligence official says the man was being courted as an informant and that it was the first time he had been brought inside the camp. An experienced CIA debriefer came from Kabul for the meeting, suggesting that the purpose was to gain intelligence, the official said.
The former intelligence official and another former official with knowledge of the attack spoke on condition of anonymity because they were not authorized to speak publicly.
The CIA would not confirm the details, and said it was still gathering evidence on the incident.
"It's far too early to draw conclusions about something that happened just yesterday," said spokesman George Little.
A separate U.S. official suggested the bomber may have set off the explosives as he was about to be searched.
The bombing on Wednesday dealt a blow to the tight-knit spy agency. Among those killed was the chief of the CIA post, whom former officials identified as a mother of three. Six more agency personnel were wounded in what was considered the most lethal attack for the CIA since the war in Afghanistan began in 2001 and possibly even since the 1983 embassy bombing in Beirut.
It also was the single deadliest attack for Americans in Afghanistan since eight soldiers were killed in an insurgent attack on a base in the east on Oct. 3.
President Barack Obama and CIA Director Leon Panetta were joined by several leading lawmakers on Thursday in praising agency employees for their work.
"Those who fell yesterday were far from home and close to the enemy, doing the hard work that must be done to protect our country from terrorism," Panetta said in a statement confirming the deaths. "We owe them our deepest gratitude, and we pledge to them and their families that we will never cease fighting for the cause to which they dedicated their lives - a safer America."
In a letter to CIA employees, Obama said their fallen colleagues came from a "long line of patriots" who had helped to keep the nation safe despite grave risks.
Obama acknowledged that the spy agency has been tested "as never before" since the attacks of Sept. 11, 2001.
Rep. Silvestre Reyes, D-Texas, who chairs the House committee that oversees intelligence, said he had met with members of the CIA team in a recent visit to Afghanistan. Reyes said the nation owes them "a great debt."
"They will forever be in my mind," he said.
The CIA did not release information about the victims, citing the sensitivity of their mission and other ongoing operations.
According to one former agency employee, the death toll represents a significant portion of the CIA's clandestine force in the region, but is unlikely to cripple the agency because so many of its employees have experience in Afghanistan.
"The bench is deeper in Afghanistan than it is anywhere in the world," the former employee said.
The bigger question for CIA operations will probably be whether the agency moves to tighten safety rules for its employees, the former employee said.
The incident occurred at a former military base on the edge of Khost city, the capital of Khost province which borders Pakistan and is a Taliban stronghold.
The Taliban claimed responsibility.
Taliban spokesman Zabiullah Mujahid said in a statement that an Afghan National Army officer wearing a suicide vest entered the base and blew himself up inside the gym. A U.S. official briefed on the blast also said it took place in the gym.
Forward Operating Base Chapman used to be a military facility base but was later turned into a CIA base, according to a U.S. official, who spoke on condition of anonymity because he was not authorized to speak publicly.
Only four known CIA operatives have been killed in Afghanistan since the 9/11 terrorist attacks in the U.S.
CIA officer Micheal "Mike" Spann was killed in a prison uprising in November 2001. An agency officer died in a training exercise in 2003, and two contractors operating out of a CIA base in Shkin district of Paktika province were killed the same year.
Adam Goldman reported from New York. Associated Press writers Matthew Lee and Anne Flaherty contributed to this report.