Noah has been having treatment in Los Angeles on his right ankle. The French team's osteopath and the Bulls' physiotherapist are said to be happy with Noah's response to treatment.
"After seeing the conclusions from the two specialists, the (Bulls) franchise doctor should give his accord for Joakim Noah to return to the France team, without having to go to Chicago," the French federation said Monday on its website.
France is training in Pau this week ahead of the European Championship. France will play Latvia on Aug. 31.
"There's been good progress, and Joakim seems to have recovered well from the little problem he had," France team director Patrick Beesley said. "I am optimistic that he will be in Pau by the end of the week."
France will play Spain in a friendly match Monday.
Noah, who sprained his right ankle playing for the Bulls in March, was also limited by a thumb injury last season. He averaged 11.7 points and 10.4 rebounds in 48 games while helping the Bulls to an NBA-best 62 wins.