Neither the Supreme Court nor Thomas's chambers would comment on the report.
The memoirs are expected to cover Thomas's career until his confirmation to the Supreme Court in 1991, including the controversy over Anita Hill's testimony during the confirmation hearings.
Hill accused Thomas of sexually harassing her when she worked for him in the 1980s, and Thomas was forced to defend himself in embarrassing public hearings before the Senate Judiciary Committee.
Thomas contended that he was the victim of an "high-tech lynching," and many Republicans branded Hill a liar. Many Democrats defended her as a victim forced to become an unwilling witness.
Thomas eventually was confirmed by a 58-42 Senate vote.
The Supreme Court's only black member, Thomas, 54, also has been one of its most conservative.
Quoting "publishing industry sources," The Washington Post reported Thursday that HarperCollins, owned by media mogul Rupert Murdoch, outbid several other companies for Thomas's book.
The Post said the book advance will be at least 4 1/2 times the size of Thomas's $184,400 annual salary.
Two other serving high court members have recently published books: Chief Justice William Rehnquist and Justice Sandra Day O'Connor. Rehnquist has written a series of historical books, including one on presidential impeachment. O'Connor has a childhood memoir, written with her brother, currently in bookstores.
The Post points out that federal judges are limited to $23,000 extra income each year, but book income is exempt from that cap.
Thomas is one of the few non-millionaires on the nine-member Supreme Court, according to annual financial disclosure reports.