The French first lady is said to have given birth at the clinic La Muette in Paris.
Quoting a “medical source” at the clinic, French newspaper Le Figaro claims that the baby is a girl, but the Elysee Palace has never publicly commented on the pregnancy, which Sarkozy, 56, and his wife regard as a private matter.
In addition, the French site Europe 1 also reports that Carla Bruni-Sarkozy has delivered a baby girl at 8p.m.
The Elysee has already warned that no official announcement would be issued after the delivery.
President Nicolas Sarkozy reportedly spent 30 minutes with his 43-year-old wife after she delivered their first child together.
He then left for a governmental meeting in Germany to discuss the euro-zone crisis with Chancellor Angela Merkel.
Carla was seen arriving at the clinic in the morning, with one member of staff confirming later: “She’s had the baby – it’s a little girl.”
This is the first baby to be born to a French presidential couple in office.
Bruni has stated in interviews that the French public has little interest in the pregnancy and that the child will never be pictured.
Sarkozy has three children from his two previous marriages, while Bruni has a son from a former relationship.