The newspaper said it confirmed Abrams and his Bad Robot production company secured the rights to "Cycle of Lies: The Fall of Lance Armstrong," which is being written by Juliet Macur, a reporter who covered Armstrong's glory days on the Tour de France for The New York Times.
Bad Robot is teaming with Paramount Pictures on the film.
"Cycle of Lies" is one of several books being penned about the doping scandal that resulted in Armstrong being stripped of his Tour titles and an Olympic medal.
Macur's book was picked up this fall by HarperCollins for a reported six-figure advance, The Hollywood Reporter said. It is slated for release in June.