The Cosatu secretary general said during the interview: "I am scared. This matter came to the public sphere three years ago, and it seems people who issued the threats then are still on a mission to attain that."
Vavi told the radio station he started receiving death threats in 2010, when he received information that he would "go down" the same way as the former deputy minister of health, Dr Molefi Sefularo.
Sefularo died in a car accident in Pretoria in 2010.
Vavi reportedly said the accident was presumed to have been "engineered".
The threat was reported to the police ministry, but nothing had come of it so far, he said.
Last year, immediately after the Cosatu held its elective congress, intelligence officials told him there was a plot by Iranians to poison him, he said.
"I was told that the plot originated from Iranian intelligence, and that someone from the non-government organisations that we, as Cosatu, work with has been hired by Iranians to poison me."
When asked why the Iranians would want him killed, Vavi said he did not know because Cosatu and the country had good relations with Iranians.
"Months have gone by and intelligence officials have not come back to me regarding this," he told Eyewitness News.
Vavi is facing an ongoing internal investigation into alleged corruption regarding the sale of Cosatu's headquarters, in which he was implicated.
Listen to the full interview: