Noah told L'Equipe newspaper he was “absolutely not ready. Not ready to run, not ready to jump.”
The 12 players who will represent France in London are set to be announced on Thursday.
It's still unclear whether San Antonio Spurs guard Tony Parker will make the cut after a scratch to his cornea in a fight involving singer Chris Brown and members of hip-hop star Drake's entourage.
France's first game at the Olympics is against the United States on July 29.