Le Journal du Dimanche said Sarkozy and Bruni, who are spending the weekend in Jordan, will wed February 8 or 9 in what would be Sarkozy's third marriage.
The Elysee Palace declined to comment. "We are not going to comment on it," the presidential office said.
The newspaper quoted Bruni's mother Marisa Borini as telling Italian press earlier: "The president has asked me for her [Bruni's] hand. I told him: 'Mr. President, I have no reason to refuse you'."
Sarkozy and Bruni met in November, shortly after the president divorced his second wife Cecilia. Since then, their relationship has been widely covered by French media.
Sarkozy assumed his office as the French president in May 2007.