The newspaper cited comments reportedly made by Donald Rickard, a former US vice-consul in Durban and CIA operative, to British film director John Irvin.
Irvin's new film "Mandela's Gun", about the months before the anti-apartheid icon's arrest, is due to be screened at the Cannes film festival this week.
Mandela was eventually freed from prison in 1990 and went on to become South Africa's president between 1994 and 1999 before dying in 2013 aged 95.
Rickard explained how Mandela was arrested as he travelled between Durban and Johannesburg but did not explain how he had learnt where he would be.
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"I found out when he was coming down and how he was coming... That's where I was involved and that's where Mandela was caught," Rickard was quoted as saying.
He added that Mandela was "completely under the control of the Soviet Union".
"He could have incited a war in South Africa, the United States would have to get involved, grudgingly, and things could have gone to hell," Rickard added.
Zizi Kodwa, national spokesman of Mandela's ruling African National Congress (ANC) party, called the revelation "a serious indictment" but said it was nothing new.
"We always knew there was always collaboration between some Western countries and the apartheid regime," he told AFP.
He claimed that though the incident happened decades ago, the CIA was still interfering in South African politics.
"We have recently observed that there are efforts to undermine the democratically elected ANC government," he alleged. "They never stopped operating here."
Rickard, who was reportedly employed by the CIA until 1978, died in March, two weeks after talking to Irvin.