In their book, Belle-Amie (Beautiful Friend), journalists Michaël Darmon and Yves Derai suggest that the father of Miss Dati’s daughter, Zohra, is Qatar’s prosecutor general, Ali Bin Fetais al-Marri. He has made no official response to the claim.
Miss Dati, 43, who has made several trips to Qatar in recent months, has declined to name the father, but told reporters that "the daddy travels a lot".
The prosecutor joins a long list of names, including leading French television host Jacques Essebag (popularly known as Arthur), Henri Proglio, a prominent Paris businessman, Dominique Desseigne, a hotel and casino tycoon, and Jose Maria Aznar, the former Spanish prime minister.
All have denied being the father but Miss Dati has said nothing. Former French rugby coach and sports minister Bernard Laporte also made an official denial, as did François Sarkozy, President Nicolas Sarkozy’s younger brother.
The new book refers to Guy de Maupassant’s 1885 novel Bel Ami, the story of journalist’s corrupt rise to power from a lowly officer to one of the most successful men in Paris, most of which he achieves by manipulating a series of powerful and wealthy mistresses.
In Belle-Amie, Miss Dati is portrayed as cynically ambitious. One high-profile publicist, Philippe Lorin, described how the young Miss Dati had befriended him and his wife, and he became her mentor.
"When my wife died in a car accident, she came to my house in the evening and we talked until three in the morning," Mr Lorin is quoted as saying. "At the end of the conversation, I told her that I was leaving Paris to live in Tangiers and that I was selling my agency.
"She disappeared from one day to the next. I obviously no longer interested her," he said. When he bumped into her years later, she blanked him, he claimed.
Miss Dati caused a stir by giving birth last month by caesarian section and returning to work five days later in time for the announcement of a major justice reform.
Popular with the French public, the glamorous minister has fallen out with the judiciary and will leave her government post after June elections for the European parliament, in which she is sure to win a seat. Mr Sarkozy reportedly gave her no choice but to accept the demotion. She is second on the ruling UMP’s electoral list for the Paris area.