People magazine said in a story on its website on Tuesday that Agassi admits to drug use in his memoir, "Open: An Autobiography," as well as talking about his hair loss and doomed marriage to actress Brooke Shields that ran from 1997 until 1999.
"I can't speak to addiction, but a lot of people would say that if you're using anything as an escape, you have a problem," he told People magazine.
People magazine and Sports Illustrated will run excerpts this week from Agassi's book which will be released by publisher Knopf on Nov. 9.
The American tennis player became a fan favourite after winning Wimbledon in 1992 when he was a cocky rebel with shoulder-length hair and went on to win the U.S. Open in 1994.
But his on-court career hit a low point in 1997 when Agassi struggled with a wrist injury and he ended the year at No. 122 in the world rankings. Publisher Knopf said Agassi reveals in his memoir that he suffered a shattering loss of confidence.
However Agassi staged a comeback from 1998 onwards, snaring a list of other titles before he finally retired after the 2006 U.S. Open.
Agassi, 39, said he was not worried about the impact of his admissions on his fans.
"I was worried for a moment, but not for long ... I wore my heart on my sleeve and my emotions were always written on my face. I was actually excited about telling the world the whole story," he said.
His memoir also talks about the love he eventually found with his current wife, retired tennis professional Steffi Graf.
(Reporting by Simon Evans in Miami; Editing by Greg Stutchbury and Belinda Goldsmith)
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