Le Point said their identities, as members of the same Darod- Majteen clan as the president, have been confirmed by several French government sources.
The report was published just hours ahead of a scheduled meeting between Ahmed and his French counterpart, Nicolas Sarkozy.
The six pirates were captured April 11, one week after hijacking the yacht Le Ponant and holding its crew of 30 for ransom.
They were arrested by a small unit of an elite French force after the ransom of about 2 million dollars was delivered and the hostages freed.
The suspects were transferred to France a few days later and an investigation was opened on charges of 'membership of a group of criminals preparing a crime,' which is punishable by a maximum sentence of 10 years in prison.
Le Point quoted a French military source as saying that the relationship of the four suspects to the Somali president was not ascertained until French diplomats asked Ahmed to allow their extradition to France.
The officer, who was not identified, said that attempts to have the captured pirates extradited were suddenly interrupted 'when Abdullah Yusuf Ahmed was informed of the names and dates of birth of four of the six pirates.'