The Taliban had claimed that the attacker was one of the group's sympathisers from the US-backed Afghan army who detonated a vest of explosives at a meeting with CIA workers at the base on Wednesday.
It was the second-most deadly attack in CIA history.
The CIA had no immediate comment on the NBC report, which identified the alleged bomber as Humam Khalil Abu-Mulal al-Balawi, 36, an Al Qaeda sympathiser from Zarqa, Jordan.
The report said Jordanian authorities believed that Al-Balawi had been successfully reformed and brought over to the American and Jordanian side. They set him up as an agent and sent him to Afghanistan and Pakistan to infiltrate al Qaeda, NBC said.
The bombing took place inside Forward Operating Base Chapman, a well-fortified compound in Khost province near the southeastern border with Pakistan.
Former intelligence officials said CIA agents at the base helped oversee strikes against Taliban and al Qaeda targets along the border between Afghanistan and Pakistan.
The security breach was a major setback to the CIA, which has been expanding its presence in Afghanistan.
Eight CIA employees were killed in a bombing of the US Embassy in Beirut in 1983.
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