Citing unnamed US and British officials, the newspaper on its website on Saturday said the Saudi government later released under the same arrangement five Britons and two others who had been convicted of crimes in Saudi Arabia.
The transfer of the five suspects from Guantanamo Bay was reportedly aimed at placating important allies in the invasion of Iraq.
The move initially met with objections from officials at the Pentagon, the Central Intelligence Agency and the Justice Department.
But the United States got promises from Saudi Arabia that the men would be kept in prison.
The Saudi prisoners were transferred to Riyadh in May 2003.
The five Britons and two other foreigners were freed subsequently in August.
The prisoner 'swap' were public relations coups for the Saudi and British governments, which had been facing domestic criticism over the Iraq war, according to the Times.
The paper said Sean McCormick, spokesman for the National Security Council, had denied that the Saudi detainees had been transferred in exchange for the Britons.
"There is no recollection here of any linkage between these two actions," he said.
Neither US nor Saudi officials would identify the five. One US official, however, said two of them had attended al-Qaida training camps in Afghanistan.
Saudi officials gave contradictory accounts of the current whereabouts of the five men, saying at first that one or two of them had been released, then denying that any had been freed.