The book's title is a reference to "You'll Never Walk Alone", a song from the Rodgers and Hammerstein musical "Carousel" that Liverpool fans adopted as a club anthem.
In a YouTube video post, Anelka said Houllier's comments were "of a racist nature" and he alleged that "it (was) not the first time".
Houllier, who led Liverpool to a League Cup, FA Cup and UEFA Cup treble in the 2000-01 season, rejected Anelka's comments.
"It is absolutely risible and ridiculous," he was quoted as saying by French sports daily L'Equipe on Sunday.
"It's false, completely false. I defy anyone to say that I am a racist with the number of black players I had the chance to work with. (Eric) Abidal, (Alou) Diarra, (Michael) Essien and so many others, you ask them."
Anelka moved to Liverpool in late December 2001 on a short-term loan, scoring five goals in a late title push which saw the Reds finish second in the Premier League.
Houllier decided against offering Anelka a permanent Anfield contract at the end of the season, instead signing Senegal's El-Hadji Diouf. The decision rankled some Liverpool supporters who were keen to see a proven goal scorer retained.
(Reporting by Julien Pretot; Editing by John O'Brien)
