The Times cited transcripts it obtained Tuesday.
U.S. law enforcement and intelligence officials told the newspaper that they would study the transcripts "because the conversations, although they are open to interpretation, could refer to the attacks on the World Trade Center and the Pentagon."
"A report by a Milan anti-terrorism prosecutor containing the transcripts suggests that Italian authorities realized sometime after Sept. 11 that the conversations could be related to the attacks on the United States," the Times reported.
The chief of the Milan office of DIGOS, Italy's anti-terrorism police, confirmed the existence of the transcripts. Massimo Mazza told The Associated Press that his office turned the transcripts over a few days ago to prosecutor Stefano Dambruoso, who is leading Italy's probe into Italian-based al Qaeda operatives.
A suspected Yemeni terrorist tells an Egyptian based in Italy about a massive strike against the enemies of Islam involving aircraft and the sky, a blow that "will be written about in all the newspapers of the world.
"This will be one of those strikes that will never be forgotten. ... This is a terrifying thing. This is a thing that will spread from south to north, from east to west. The person who came up with this program is a madman from a madhouse, a madman but a genius. He is fixated on this program; it will leave everyone turned to ice," according to the transcript obtained by The Times.
"That dialogue took place Aug. 12, 2000, in a Citroen driven by Abdelkader Mahmoud Es Sayed, then 39, an Egyptian accused of being Al Qaeda's top operative in Italy and a man with ties to the inner circle of Osama bin Laden. Es Sayed had just picked up the Yemeni, Abdulsalam Ali Ali Abdulrahman, at the Bologna airport," the newspaper reported, citing a transcript contained in a report by the Milan prosecutor.
"In the future, listen to the news and remember these words: Above the head ... remember well, remember well- The danger in the airports- There are clouds in the sky there in international territory, in that country, the fire has been lit and is awaiting only the wind," the Yemeni was reported as saying.
Authorities eavesdropped on the two by bugging places where they were, not by tapping telephone lines; it took a long time to remove extraneous noise from the recordings and translate them, Mazza said.
The Milan daily newspaper Corriere della Sera, which also published excerpts of the transcripts, reported that the FBI helped Italian experts to decipher the bugged conversations.
Before Sept. 11, investigators had few clues about what the men might be discussing, Mazza told the AP. "After what happened, it's now easy to draw conclusions ... but before, it was difficult to understand."
The leaders of the Sept. 11 plot were based in Hamburg, Germany, and trained along with the rest of the 19 hijackers at U.S. flight schools.
One of the suspects, Es Sayed, has been known to U.S. law enforcement for some time, the Times reported.
Es Sayed was named in an April 19 order by the Treasury Department blocking the assets of suspected terrorists. He was also convicted in Egypt in connection with the 1997 massacre of 58 foreign tourists at Luxor, and he was wanted in Italy on charges of conspiring to traffic in arms, explosives, chemical weapons and identity papers and aiding illegal immigration.
Es Sayed fled Italy to Afghanistan in July 2001, after Italian police rounded up his accomplices in a Tunisian-dominated network accused of plotting against U.S. targets, according to the newspaper.