The planned strikes were aimed at Iranian military facilities, The New York Times reported, adding that Netanyahu and Barak, who is also a former Israeli prime minister, approached the idea of striking in 2010, 2011 and 2012.
"In 2010, the military chief of staff said Israel lacked the 'operational capability'; in 2011, two key ministers waffled at the last minute; and in 2012, the timing did not work out because of a joint United States-Israel military exercise and visit by the American defense secretary," the news organization reported.
The Times said it spoke with Barak, who confirmed the authenticity of the audio.
Barak wanted to prevent the audio from being aired, pointing to military censorship, but the military then approved the material, according to the Jerusalem Post, which cited Channel 2.
CNN is reaching out to the parties involved and to the Israeli government for comment.