Zohra Dati may be only a few days old but she is already a celebrity, with a page on Facebook and her short life story the subject of intense speculation in the press and on the internet.

She owes her status in large measure to her mother, Rachida Dati, France’s glamorous Justice Minister who has rarely been out of the headlines since she became a symbol of ethnic diversity when she was appointed to President Sarkozy’s Cabinet in 2007.

Miss Dati can also thank her father for making her one of the most famous babies in recent French history however – his identity has sent the Parisian rumour-mill spinning. After months of gossip François Sarkozy, the younger brother of the President, was seen at the private Muette Clinic last night, adding to persistent although unconfirmed claims that he is le père. A source told The Timesthat he had visited Ms Dati with Guillaume Sarkozy, the President’s older brother.

Mr Sarkozy, 47, a pharmaceutical industrialist, is reported to have spent Christmas with Ms Dati. Their liaison, if confirmed, may explain why the President appears reluctant to dismiss Ms Dati, 43, despite criticism of her performance at the Justice Ministry.

Officials refused to comment on speculation about the father last night.

Zohra, who was born on Friday, was reportedly registered under the name of her mother only.

José MarÍa Aznar, the former Spanish Prime Minister, Bernard Laporte, the French Sports Minister, and Dominique Desseigne, the chairman of the Barrière casino and hotel group, have all publicly denied being the father.

One rumour suggested that Mr Sarkozy was le géniteur but it appears farfetched and another claimed that Ms Dati became pregnant after receiving an anonymous sperm donation.

This, too, seems unlikely because fertility treatment is reserved for couples under French law. Despite reports that she was ready to leave politics for a job with the French oil group Total, Ms Dati appeared determined to cling to her job.

Her spokesman said that she had returned to her ministerial papers within hours of having her baby delivered by Caesarean section and would be back in her office as soon as possible.

“She wants to be absent for a very short time,” he said. “Clinic or not, she is following the ministerial agenda.”

Ms Dati had said previously that she would take only a week off work. A Justice Ministry source said that the minister wanted to be present when Mr Sarkozy delivers a speech on Wednesday to the Cour de Cassation, the highest French court.

The President is understood to be keen to move Ms Dati from the Justice Ministry, where her high-handed style has infuriated lawyers and judges. Her status as France’s best known Arab politician and determination to continue working have made dismissal unlikely however.

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