Rodriguez, the Yankees' third baseman, is already under a cloud after admitting earlier this year to using steroids between 2001-03, when he played for the Texas Rangers - and when they were not banned by Major League Baseball.
Roberts, who broke the story on that scandal, quotes former players and acquaintances saying that Rodriguez's involvement with performance enhancing drugs apparently started earlier -- and continued far later.
Rodriguez declined to address the latest allegations.
"I'm not going there," he said after homering in an extended spring training intra-squad game in Tampa, Florida, part of his rehabilition after hip surgery. "I'm just so excited about being back on the field and playing baseball."
Ex-teammate Jose Canseco is quoted as saying that steroid could have begun in high school in Miami, where Rodriguez put on 25 pounds (11.3 kilos) of muscle in one year.
"I worked out with him when he was 18. He could lift almost as much as I could," Canseco said, the Daily News reported.
Roberts quotes a former high school teammate saying that the coach knew the future Major League Baseball star was taking steroids.
More recently, Rodriguez raised eyebrows at the Yankees when he put on 15 pounds (6.8 kilos) in the off season in 2005, the book claims.
"No one ever asked Alex directly that I know of, but there was a lot of suspicion in house," a Yankee employee is quoted as saying, according to the Daily News.
Rodriguez, a three-time American League Most Valuable Player, is is expected to rejoin the Yankees in mid-May.
He said he wasn't worried that the doping issue had resurfaced.
"I'm in a good place," he said. "I think more importantly, physically I feel like I'm getting better every day.
"We've had a great week here. We've worked extremely hard, and I'm just very anxious to do what God put me on this earth to do, to play baseball."
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