Bruni-Sarkozy is in her eighth month of pregnancy and, according to newspaper Le Parisien, her doctors have advised her against travelling.
"She is 43 and this is a late pregnancy. She's been trying to have a second child for a long time and it's normal to take every precaution," a childhood friend told Le Parisien.
Bruni-Sarkozy shared her own frustrations about the pregnancy with a group of students last week.
The First Lady was at the Galerie Nikki Diana Marquardt in Paris to meet students who receive financial support from her own foundation to help them with artistic studies.
"Honestly, I can't do it any more," she told them. "I have to sit down or lie down most of the time. I can't smoke or drink wine. I can't wait for it to end. After October 1st it could happen at any moment and my first child, Aurélien, arrived early. It's long, but I really wanted this."
Bruni-Sarkozy said in a recent interview that she did not know whether she was expecting a boy or a girl. She also said she will fiercely protect the child's privacy when he or she is born.
President Sarkozy has a busy schedule in New York, starting on Tuesday with a meeting with Mahmoud Abbas, president of the national Palestinian authority.
He will meet US president Barack Obama on Wednesday afternoon.