The Briton fell in training last Wednesday and suffered multiple serious injuries that required over six hours of surgery.
The source at Saint-Etienne hospital told AFP Froome would leave intensive care in the coming days, most likely Saturday, but would continue more conventional treatment on another ward.
The news comes on the same day reigning Tour de France champion, Froome's Ineos teammate Geraint Thomas, was sent to hospital in Switzerland after hurting his shoulder in a fall in the Tour de Suisse.
Froome, 34, was airlifted to hospital in Saint-Etienne for emergency surgery after slamming into a wall at high speed during practice on Wednesday ahead of the fourth stage of the Criterium du Dauphine race in central France.
The force of the impact fractured his pelvis, right femur, hip, right elbow and left him with broken ribs.
"I know how lucky I am to be here today and how much I owe to all the paramedics and medical staff on the race," said Froome.
Froome will miss out on a chance to win a record-equalling fifth Tour de France title next month, but after successful surgery there is hope he could return to cycling in six months.