The official, who spoke on Friday on condition of anonymity, did not provide more details about the US national, who he said was among the 7-10 people captured during the summer of 2002.
Saudi Aramco is the Saudi Arabian state-owned oil company and a spokesman in Houston could not immediately be reached for comment.
Adil al-Jubair, foreign policy adviser to Saudi Crown Prince Abd Allah bin Abd al-Aziz, told reporters in Washington his country had taken many steps to fight “terrorism” including more restrictions on financial flows.
Saudi authorities have detained "well over 500 people" who are “terrorism” suspects, he said.
"We have contributed to stifling operations not just in Saudi Arabia but in other countries, including in the United States"
foreign policy adviser to
Crown Prince Abd Allah
"We have stifled a number of operations, terrorist operations," Jubair said.
"We have contributed to stifling operations not just in Saudi Arabia but in other countries, including in the United States," he added.
Reacting to the Saudi revelation, a federal law enforcement official in Washington said the FBI did not have any information about a US national in custody in Saudi Arabia related to such an incident.
The US government originally brought that individual, who was of Saudi origin with an American passport, to the attention of the kingdom's authorities, the US source said on condition of anonymity.
Since the 11 September, 2001 attacks in which 15 of the 19 hijackers were said to be Saudis, the Saudi government has been trying to overcome a perception that it was too lax about hardliners inside its borders.